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Topic: Norm topology

Related Topics

Weak topology

Topologies on the set of operators on a Hilbert space

Exponential (category theory)

Topology

Jordan curve theorem

Enterobius vermicularis

	Topologies on the set of operators on a Hilbert space - Wikipedia, the free encyclopedia
		The norm topology or uniform topology or uniform operator topology is defined by the usual norm
		The weak topology is useful for compactness arguments as the unit ball is compact.
		The weak and strong topologies are widely used as cheap approximations to the ultraweak and ultrastrong topologies, and the remaining topologies are of little practical importance.
	en.wikipedia.org /wiki/Topologies_on_the_set_of_operators_on_a_Hilbert_space (904 words)

	Encyclopedia: Norm (mathematics) (Site not responding. Last check: 2007-10-09)
		In linear algebra, functional analysis and related areas of mathematics a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector.
		is a rhomboid, for the 2-norm (Euclidean norm) it is the well-known unit circle, while for the infinity norm it is a square.
		In terms of the vector space, the semi-norm defines a topology on the space, and this is a Hausdorff topology precisely when the semi-norm can distinguish between distinct vectors, which is again equivalent to the semi-norm being a norm.
	www.nationmaster.com /encyclopedia/Norm-%28mathematics%29 (2560 words)

	Encyclopedia: Metric space (Site not responding. Last check: 2007-10-09)
		In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
		Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces.
		Topology Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Thales (circa 624-547 BC) dealing with spatial relationships.
	www.nationmaster.com /encyclopedia/metric-space (4019 words)

	Strong operator topology - Encyclopedia, History, Geography and Biography
		In functional analysis, the strong operator topology, often abbreviated SOT, is the weakest topology on the set of bounded operators on a Hilbert space such that the evaluation map sending an operator T to the real number $\Tx\$ is continuous for each vector x in the Hilbert space.
		The SOT is stronger than the weak operator topology and weaker than the norm topology.
		The SOT topology also provides the framework for the measurable functional calculus, just as the norm topology does for the continuous functional calculus.
	www.arikah.net /encyclopedia/SOT (346 words)

	RFC 3940 (rfc3940) - Negative-acknowledgment (NACK)-Oriented Reliable Mult
		NORM can make use of reciprocal (among senders and receivers) multicast communication under the Any-Source Multicast (ASM) model defined in RFC 1112 [3], but SHALL also be capable of scalable operation in asymmetric topologies such as Source Specific Multicast (SSM) [14] where there may only be unicast routing service from the receivers to the sender(s).
		NORM protocol implementations may offer either (or both) in-order delivery of the stream data to the receive application or out-of-order (more immediate) delivery of received segments of the stream to the receiver application.
		NORM NormObjectTransportId data content identifiers are sender-assigned and applicable and valid only during a NormObject's actual _transport_ (i.e., for as long as the sender is transmitting and providing repair of the indicated NormObject).
	www.faqs.org /rfcs/rfc3940.html (15244 words)

	Strong operator topology -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		The SOT is (additional info and facts about stronger) stronger than the (additional info and facts about weak operator topology) weak operator topology and weaker than the (additional info and facts about norm topology) norm topology.
		On the other hand, the SOT topology provides the natural language for the generalization of the (additional info and facts about spectral theorem) spectral theorem to infinite dimensions.
		The SOT topology also provides the framework for the (additional info and facts about measurable functional calculus) measurable functional calculus, just as the norm topology does for the (additional info and facts about continuous functional calculus) continuous functional calculus.
	www.absoluteastronomy.com /encyclopedia/s/st/strong_operator_topology.htm (396 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Experimental [Page 17] RFC 3940 NORM Protocol November 2004 offset values, but instead are values computed from FEC encoding the "payload_len" and "payload_offset" fields of the _source_ data symbols of the corresponding applicable coding block.
		Experimental [Page 20] RFC 3940 NORM Protocol November 2004 course of its transmission within a NORM session, an object is uniquely identified by the concatenation of the sender "source_id" and the given "object_transport_id".
		Experimental [Page 22] RFC 3940 NORM Protocol November 2004 field is used by the sender to indicate the size of its stream buffer to the receiver group.
	mirror.aarnet.edu.au /pub/rfc/rfc3940.txt (14782 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The topology defined by the norm is called the {\it norm}~\index{topology!norm} or {\it uniform topology}~\index{topology!uniform}.
		When thought of as a space of maximal ideals, $\hc$ is given the {\it Jacobson topology}~\index{Jacobson topology} (or {\it hull kernel topology}) producing a space which is homeomorphic to the one constructed by means of the Gel'fand topology.
		In this topology, a subset $S \subset \ha$ is open if and only if is of the form $\{ \pi \in \ha ~~ ker(\pi) \in W \}$ for some subset $W \subset \prim$ which is open in the (Jacobson) topology of $\prim$.
	www.ma.utexas.edu /mp_arc/papers/97-62 (9392 words)

	Weak operator topology -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		The WOT is weaker than the (additional info and facts about strong operator topology) strong operator topology and weaker than the (additional info and facts about norm topology) norm topology.
		The (additional info and facts about weak-star topology) weak-star topology is stronger than the WOT.
		The (additional info and facts about linear functional) linear functionals on the set of bounded operators on a Hilbert space which are continuous in the (additional info and facts about strong operator topology) strong operator topology are precisely those which are continuous in the WOT.
	www.absoluteastronomy.com /encyclopedia/w/we/weak_operator_topology.htm (192 words)

	[No title]
		The relative weak topology on $\al G.$ seems to be easier for construction of models where the action of $K$ on $\al F.$ is continuous.
		Moreover this topology is not obviously natural from the viewpoint of gauge groups acting by automorphisms of operator algebras.
		The relative weak topology on the group $C(X,U(n))$ is more interesting, because it is actually finer than both the Bohr topology and the topology of convergence in measure.
	www.ma.utexas.edu /mp_arc/e/04-14.latex.mime (3467 words)

	Topology
		The family t is called a topology (for X) when it satisfies these axioms and its elements are called _open sets_ (open wrt the topology).
		Call a topology t _stronger_ than the topology t' (both for the same set X) if t is contained in t'.
		It follows that the density theorem for neural network functions wrt sup norm topology implies that it holds for any L_p-topology, for p strictly between 1 and oo.
	www.georgetown.edu /faculty/kainen/topology.html (1132 words)

	A Hilbert space (Site not responding. Last check: 2007-10-09)
		(iii) the operator norm is not continuous with respect to the strong operator topology and the weak operator topology;
		Hence (i) implies that the weak operator topology and the strong operator topology don't coincide on B(H).
		Therefore the operator norm is not continuous on B(H).
	web.um.ac.ir /~moslehian/cfa/Ot15.htm (309 words)

	Spectral Approximation of Multiplication Operators - Morrison (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators.
		Multiplication operators on spaces of L 2 functions are never compact; for them we consider how well the eigenvalues of the matrices approximate the spectrum of the multiplication operator, which is the essential range of the multiplier.
		Norms of Inverses, Spectra, and Pseudospectra of Large..
	citeseer.ist.psu.edu /morrison95spectral.html (668 words)

	Weak operator topology (Site not responding. Last check: 2007-10-09)
		In functional analysis, the weak operatortopology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space such that the functional sending an operatorT to the complex number
		The WOT is weaker than the strong operatortopology and weaker than the norm topology.
		The linear functionals on the set of bounded operators on aHilbert space which are continuous in the strongoperator topology are precisely those which are continuous in the WOT.
	www.therfcc.org /weak-operator-topology-329537.html (158 words)

	R. Lowen (Site not responding. Last check: 2007-10-09)
		Topology Atlas Conference Abstracts Document # caai-68.htm
		Considering these structures on E and E' we are able to extend important fundamental results in functional analysis to "approximation versions" of these results.
		Thus we are able to prove new characterizations of the dimension, completeness and reflexivity of normed spaces, we obtain Tschebyscheff-type approximation formulas between the various types of convergences on E, E' and E", and making use of the measure of compactness of the unit ball we obtain a 0-1 law for reflexivity.
	www.utm.edu /staff/jschomme/topology/c/a/a/i/68.htm (84 words)

	APPENDIX A
		A norm determines the norm topology by the open ball neighborhoods of x with radius a.
		The open sets of the norm (uniform) topology of Alg are once again, generated by the open balls of the induced norm.
		The norm topology is stronger (= finer = "has more open sets" = "fewer convergent sequences") than the strong operator topology.
	graham.main.nc.us /~bhammel/SPDER/apdxA.html (1576 words)

	Re: Topology of Hilbert (Quantum State) Spaces
		From some things I have been >reading, I've got the impression the (differential?) topology of M can >be reconstructed from the orthogonal basis for the Hilbert space H >diagonalizing the position operators.
		If we use the norm topology, it certainly doesn't work, >as the vectors in the basis are orthogonal, and thus lie in a certain >(infinite!
		Of course, physicists act like they do, which is fine some of the time, but since you're asking a very mathematical question involving topologies and all that jazz, I really can't answer it without being mathematical.
	www.lns.cornell.edu /spr/2000-03/msg0023078.html (391 words)

	Curriculum Vitae of Taehee Kim (Site not responding. Last check: 2007-10-09)
		The twisted Alexander polynomial and the Thurston norm
		Conference on Low-Dimensional Topology, University of Virginia, Charlottesville, December, 2004.
		Topology Seminar, University of Illinois at Urbana-Champaign, October 15, 2002.
	math.rice.edu /~tkim/resume.html (400 words)

	PlanetMath: differentiable function
		is treated as a Banach space under the usual Euclidean vector norm.
		with respect to one norm, it is differentiable with
		The way to proceed is to pick a norm, any norm
	planetmath.org /encyclopedia/DifferntiableFunction.html (380 words)

	Kit Chan's Annotated Bibliograhy
		On a separable infinite dimensional complex Hilbert space, we show that the set of hypercyclic operators is dense in the strong operator topology, and moreover the linear span of hypercyclic operators is dense in the operator norm topology.
		Our works make connections with the classical result on the nondenseness of cyclic operators in the operator norm topology, as well as the recent development on hypercyclic subspaces.
		In the present paper, we obtain an analogous sufficient condition when X is one nonmetrizable space, namely the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology.
	personal.bgsu.edu /~kchan/docs/biblio.html (1091 words)

	COUNTEREXAMPLES IN OPERATOR THEORY (Site not responding. Last check: 2007-10-09)
		Operators of arbitrary large norms that are bounded by 1 on a given basis of a separable infinite dimensional Hilbert space H. OT12.dvi
		A sequence of quasi-nilpotent operators acting on a Hilbert space with a norm limit whose spectral radius is 1.
		A sequence of nilpotent operators on H which converges with respect to the norm topology on B(H) to an operator which is not topologically nilpotent.
	web.um.ac.ir /~moslehian/cfa/OT.HTM (454 words)

	PlanetMath: sphere
		In topology and other contexts, spheres are treated slightly differently.
		In topology we usually fail to distinguish homeomorphic spaces, so all homeomorphic images of
		Cross-references: clear, images, homeomorphic, manifold, unit, unit circle, real, subset, Euclidean norm, norm, topology, bound, side, Proportion, infinity, gamma function, line, circle, formula, radius, length, origin, equation, dimensions
	planetmath.org /encyclopedia/Sphere.html (345 words)

	Atlas: Renormings and coverings in Banach spaces by J. Orihuela
		Consequently every Banach space with a locally uniformly rotund norm has a network for the norm topology which is \sigma -half-space isolated.
		For instance we will show how a weakly locally uniformly rotund norm gives us a \sigma -half-space isolated network for the norm topology and consequently that it is locally uniformly rotund renormable, [2].
		Therefore in spaces with the RNP to have an equivalent locally uniformly rotund norm or to have an equivalent Kadec norm are the same.
	atlas-conferences.com /cgi-bin/abstract/caey-75 (408 words)

	The decomposition of the spacetime into p-adic regions with various values of the p-adic prime
		Ultrametricity implies that the norm of even of an infinite sum of p-adic numbers cannot be larger than the maximum of the norm for the individual summands.
		The hypothesis that the topology of a given spacetime sheet of the effective, quantum average spacetime surface (whatever it means!) is p-adic rather than real, is much stronger requirement than p-adicity of the topology of the energy landscape.
		Effective p-adic topology and p-adic pseudo constants indeed make it possible to avoid large surface energies since everything is continuous and even differentiable with respect to the p-adic topology.
	www.sci.fi /~jawap/colors/string/spin.html (4171 words)

	RePEc
		Abstract: An extension of Berge's Maximum Theorem is given, with two different topologies on the choice set used for the two semicontinuity assumptions on preferences.
		Though that result provides a sufficient basis for the direct, excess-demand method of proving equilibrium existence, its usefulness is limited by the extreme strength of the finite topology.
		With the norm topology used instead, demand continuity acquires an independent interest, particularly for practical implementations of the equilibrium solution.
	www.inomics.com /cgi/repec?handle=RePEc:cep:stitep:246 (219 words)

	Georgia Tech Colloquium Abstracts (Site not responding. Last check: 2007-10-09)
		In my talk I outline evolution of topology in which this formula is proved on the examples of contraction and Gibbs semigroups.
		A real breakthrow in this subject is dates by 1993, when Rogava announced that for self-adjoint contraction semigroups the Trotter product formula converges in the uniform, instead of the strong topology, as it was known since the Trotter paper.
		One of the recent result in this direction (2001) is the ultimate optimal opeartor-norm estimate of the convergence-rate of the Trotter formula for the self-adjoint contractions, and the corresponding result for the Gibbs semigroups in the trace-norm topology.
	www.math.gatech.edu /~mccuan/abstracts/zagrebnov.html (128 words)

	[No title]
		More precisely, if we have a new vector space topology on $E$, and if the bounded sets associated to this topology are the same as those of the initial $E$, then the classes $\Lambda^s$ and $\Lip^{(k)}$ are also the same.
		For example the weak $\Lambda^s$ class (obvious definition) coincides with the norm $\Lambda^s$ class; or if $E$ is an adjoint space, then the weak* $\Lambda^s$ class coincides with the norm $\Lambda^s$ class.
		In other terms, it is the topology associated to the family of seminorms $T\mapsto \langle g,Tf\rangle$ with $f\in \C{H}_{s,p}$ and $g\in \C{H}_{-t,q'}$.
	www.ma.utexas.edu /mp_arc/papers/97-428 (8568 words)

	Functional Analysis Unit 2 (Site not responding. Last check: 2007-10-09)
		Being a union of a convergent (by norm) sequence and its limit, A is obviously compact.
		Therefore it is norm bounded which gives the rigth estimate in (2).
		is equivalent to the norm induced by (.,.).
	mystic.math.neu.edu /courses/funcan/unit2 (622 words)

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