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	Reflexive space - Wikipedia, the free encyclopedia
		All Hilbert spaces are reflexive, as are the L
		A space is reflexive if and only if its unit ball is compact in the weak topology.
		A Banach space X is reflexive iff each linear bounded functional defined in X attains its maximum on the unit ball of X (Famous James Theorem).
	en.wikipedia.org /wiki/Reflexive_space (364 words)

	Polynomially reflexive space - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, a polynomially reflexive space is a Banach space X, on which all polynomials are reflexive.
		is identical to the dual space, and is thus reflexive for all reflexive X.
		This implies that reflexivity is a prerequisite for polynomial reflexivity.
	en.wikipedia.org /wiki/Polynomially_reflexive_space (162 words)

	Reflexive space: Definition and Links by Encyclopedian.com - All about Reflexive space (Site not responding. Last check: 2007-11-06)
		In functional analysis, reflexive spaces are certain Banach spaces which are defined by some abstract property of dual spaces and turn out to have desirable geometric properties.
		More generally: all uniformly convex[?] Banach spaces are reflexive.
		A space is reflexive if and only if its dual is reflexive.
	www.encyclopedian.com /re/Reflexive-space.html (248 words)

	Reflexive space -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		The space X is called reflexive if J is (Click link for more info and facts about bijective) bijective.
		A space is reflexive if and only if its unit ball is (A small cosmetics case with a mirror; to be carried in a woman's purse) compact in the (Click link for more info and facts about weak topology) weak topology.
		A reflexive space is (Click link for more info and facts about separable) separable if and only if its dual is separable.
	www.absoluteastronomy.com /encyclopedia/R/Re/Reflexive_space.htm (586 words)

	PlanetMath: dual space
		For example, any finite dimensional space is reflexive, and any Hilbert space is reflexive by the Riesz representation theorem.
		A related notion is the duality in projective spaces.
		This is version 10 of dual space, born on 2002-02-03, modified 2004-09-17.
	planetmath.org /encyclopedia/DualSpace.html (235 words)

	Banach space - FreeEncyclopedia (Site not responding. Last check: 2007-11-06)
		If V is a Banach space and K is the underlying field (either the real or the complex numbers), then K is itself a Banach space (using the absolute value as norm) and we can define the dual space V' by V' = L(V, K).
		A space is reflexive if and only if its dual is reflexive, which is the case if and only if its unit ball is compact in the weak topology.
		R or the space of all distributions on R, are complete but are not normed vector spaces and hence not Banach spaces.
	openproxy.ath.cx /ba/Banach_space.html (1002 words)

	LMS Proceedings Abstract, paper PLMS 1383 (Site not responding. Last check: 2007-11-06)
		The set of normalizers between von Neumann (or, more generally, reflexive) algebras $\mathcal{A}$ and $\mathcal{B}$ (that is, the set of all operators $T$ such that $T \mathcal{A} T^{\ast} \subseteq \mathcal{B}$ and $T^{\ast} \mathcal{B} T \subseteq \mathcal{A}$) possesses 'local linear structure': it is a union of reflexive linear spaces.
		Such a space is reflexive whenever it is ultraweakly closed, and then it is of the form $\mathcal{U} = \{T : TL = \phi (L) T$ for all $L \in \mathcal{L}\}$ where $\mathcal{L}$ is a set of projections and $\phi$ a certain map defined on $\mathcal{L}$.
		Normalizing spaces which are bimodules over maximal abelian self-adjoint algebras consist of operators 'supported' on sets of the form $[f = g]$ where $f$ and $g$ are appropriate Borel functions.
	www.lms.ac.uk /publications/proceedings/abstracts/p1383a.html (205 words)

	Most Recent Preprints (Site not responding. Last check: 2007-11-06)
		Stabilization of Tsirelson-type norms on $\ell_p$ spaces by Anna Maria Pelczar.
		A universal reflexive space for the class of uniformly convex Banach spaces by E. Odell and Th.
		Lipschitz spaces and $M$-ideals by Heiko Berninger and Dirk Werner.
	www.math.okstate.edu /~alspach/banach/recent.html (4178 words)

	imagination.html
		This formulation of a positive non-Euclidean space is the later foundation of a physics based on space-curvature, an expanding universe, and a general theory of the self-development of energy.
		A curved space is a self-reflexive space, a space-time in which infinity is present in self- development.
		Although not self- reflexive (Erigena places nature which both creates and is created on a lower level) we see in theological form an anticipation of Hegel's world spirit, an in-and-for-itself subject which is the object of its own activity (22).
	home.earthlink.net /~lrgoldner/imagination.html (5752 words)

	56 #2891
		Since the property of being single is purely algebraic, while the property of being rank-one is a spatial concept, the relationship between rank-ones and single operators may throw light on the connection between the algebraic and spatial structures of the algebra.
		A new proof is given of the density of the finite-rank operators in the unit ball of a certain reflexive algebra of operators, and a similar result is obtained for some reflexive algebras with finite atomic lattices of invariant subspaces.
		The last part of the paper concerns operators in a Hilbert space that allow spectral synthesis (that is, every invariant subspace of the operator is the span of root vectors corresponding to nonzero eigenvalues).
	www.math.uoc.gr /~lambrou/MR.htm (4146 words)

	An Introduction to Banach Space Theory
		Section 1.12, devoted to separability, includes the Banach-Mazur characterization of separable Banach spaces as isomorphs of quotient spaces of \ell_1, and ends with the characterization of separable normed spaces as the normed spaces that are compactly generated so that the stage is set for the introduction of weakly compactly generated normed spaces in Section 2.8.
		The goal of optional Section 2.9 is to obtain James's characterization of weakly compact subsets of a Banach space in terms of the behavior of bounded linear functionals.
		Schauder's theorem relating the compactness of a bounded linear operator to that of its adjoint is presented, as is the characterization of operator compactness in terms of the bounded-weak*-to-norm continuity of the adjoint.
	www.math.lsa.umich.edu /~meggin/ibst.html (2875 words)

	Reflexive space (Site not responding. Last check: 2007-11-06)
		For Halmos ' notion of the reflexivity of an operator algebra or a subspace lattice, see Reflexive operator algebra.
		This isagain a Banach space, as explained in the dual space article.
		The promised geometric property of reflexive spaces is the following: if C is a closed non-empty convex subset of the reflexive space X, then for every x in X thereexists a c in C such that
	www.therfcc.org /reflexive-space-195560.html (265 words)

	Scholia Reviews ns 14 (Site not responding. Last check: 2007-11-06)
		In dealing with each of the plays he draws on six spatial categories that he regards as basic to the Theatre of Dionysus: (i) theatrical space, (ii) scenic space, (iii) extra-scenic space, (iv) distanced space, (v) self-referential space, and (vi) reflexive space.
		In turning to the theme of space itself Rehm illustrates his first category, space for homecomings, with a close analysis of Oresteia and Heracles Mainomenos (although he takes care to point out that there are several other tragedies where return forms an element within the action).
		In dealing with eremetic space Rehm concentrates on the desolation that takes the stage in Antigone -- how this resonates through the play in reality and image -- and in Ajax with both its shift to the emptiness of the sea shore and the hero's increasing isolation from his family.
	www.classics.und.ac.za /reviews/05-20reh.htm (929 words)

	ALL COUNTEREXAMPLES (Site not responding. Last check: 2007-11-06)
		A Banach algebra A that cannot be a (vector space) direct sum of its radical Rad(A) and a Banach algebra B that is homeomorphically isomorphic with A/Rad(A).
		A primitive C-algebra A acting on a Hilbert space* H such that the intersection of A and A' is {0}.
		A sequence of quasi-nilpotent operators acting on a Hilbert space with a norm limit whose spectral radius is 1.
	web.um.ac.ir /~moslehian/cfa/ALL.HTM (1368 words)

	LaTeX bugs database
		As $E_{\b \b}''$ is the strong dual of a metrizable space, it is barrelled and bornological (\cite{jar}, Corollary 13.4.4).
		%By (\cite{din}, Proposition 1.35) $(\sP(^nE),\t_b)$ is a DFM space, %and consequently is reflexive.
		As a countable inductive limit of Banach spaces $E_{\b \b}''$ is a barrelled DF space, hence $E_\b'$ is a distinguished Fr\'echet space and by (\cite{din1}, Corollary 1.53) $\pi_w=\pi_b$ on $ \sP_N(^nE_\b')$.
	www.latex-project.org /cgi-bin/ltxbugs2html?pr=latex/3560 (7944 words)

	Quantum Feminist Mnemotechnics: Guertin's Dissertation Abstract
		Always in flux, the shape of time's transformation is a Möbius strip unfolding time into the dynamic space of the postmodern text, into the 'unfold.' As quantum interference, the unfold is a gesture that is a sensory interval.
		In this in-between space, the transformance of the nomadic browser takes place; she performs the embodied knowledge acquired in her navigation of the world of the text.
		Quantum space in hypertexts is shaped as an irreducible knot, an entangled equation both in and out of space-time, spanning all dimensions as a node in a mnemonic system.
	www.mcluhan.utoronto.ca /academy/carolynguertin/abstract.html (847 words)

	FuncAna
		Dual space of normed vector space is a Banach space.
		Local weak compactness of the dual spaces of normed vector spaces: closed bounded sets in the dual space are weakly compact.
		Orthogonal sum decomposition of the space in terms of the null spaces and ranges of an operator and its adjoint.
	www.math.ttu.edu /~vshubov/FuncAna/FuncAna.html (947 words)

	BGU Set Theory and Topology Seminars
		Abstract: A flow is, by the definition, an action of G on a topological space X, where G is either the group of integers or the group of the real numbers; we add the adjective discrete or continuous to specify the group.
		An interesting problem is which topological spaces admit minimal flows (a flow is minimal if all its orbits are dense).
		Finally, I will prove that if a Hausdorff space X admits a flow whose all forward orbits are dense then X is either compact or else X is nowhere locally compact.
	www.math.bgu.ac.il /~arkady/topologyseminar/topologyseminararchive.htm (543 words)

	Math218
		Let M be a closed proper subspace of a normed space X. Then there exists a continuous linear functional of norm one, vanishing on M. Proof.
		The weak topology on a normed space X is Hausdorff (in particular, bounded linear functionals on X separate points).
		Denseness of C_c^\infty and of the Schwartz space in L^p and in C_0.
	math.vanderbilt.edu /~neamtu/330a/final_b.html (554 words)

	Publications of G.Ya.Lozanovsky
		[35] (with A.I. Veksler and A.V. Koldunov) On the local construction of spaces of measurable functions on the space of maximal ideals of the Banach algebra L^infty (Russian).
		Notes 20 (1976), 969-973, as The continuation of linear functionals in Banach spaces of measurable functions.
		[50] On the conjugate space of Banach lattice (Russian).
	www.mathsoc.spb.ru /pers/lozanovs/bib.html (784 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Every reflexive space satisfies existence of a proximinal point (because the norm is sequentially weakly lower semi-continuous), and the strict convexity guarantees uniqueness.
		If it's supposed to be, "If X is a Banach space with the property that every closed nonempty subset E with the property that each x in X has a unique proximinal point in E ==> E must be convex then X is a Hilbert space", then yes, I believe this is still open.
		The converse (by which I suppose you mean "every Chebyshev set in a Hilbert space in convex", where E is a Chebyshev set in H provided for every point x in H there is a unique point in E that is of minimal distance from x) is still unsolved.
	www.math.niu.edu /~rusin/known-math/00_incoming/hilb_char (363 words)

	Haskell Rosenthal: Research
		An operator space is a closed linear subspace X of B(H) along with the natural spatial tensor norm induced on K
		The structure of operator spaces with the Complete Separable Complementation Property (CSCP) is studied in [85] and [86].
		In a different direction, the work in [94] initiates the study of operators with substantial invariant subspaces, that is, invariant (closed) subspaces of infinite dimension and codimension.
	www.ma.utexas.edu /users/rosenthl/in-progress/in-progress.html (558 words)

	Operator Topologies and Reflexive Representability - Megrelishvili (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		We show that if a Banach (or, even, Frechet) space X has the Radon-Nikodym property RNP, then the weak and strong operator topologies coincide on every bounded (respectively, equicontinuous) subgroup G of GL(X).
		3 The duality between Asplund spaces and spaces with the Radon..
		1 A geometric characterization of Banach spaces possessing the..
	citeseer.ist.psu.edu /megrelishvili00operator.html (726 words)

	RESEARCH PUBLICATIONS (Site not responding. Last check: 2007-11-06)
		M.A. Smith, A reflexive Banach space that is LUR and not 2R Canad.
		M.A. Smith and B. Turett, A reflexive LUR Banach space that lacks normal structure Canad.
		Z. Hu and M. Smith, On the extremal structure of the unit ball of the space C(K,X)* Function Spaces, the second conference, Lec.
	www.users.muohio.edu /smithma/publications.html (332 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Your identity says X^* is reflexive, but X is reflexive if and only if X^* is reflexive: see e.g.
		Date: Mon, 18 May 1998 10:03:41 -0400 > edgar@math.ohio-state.edu (G. Edgar) wrote: > > > However, I think the James space J may be constructed without choice, > > and in that example J**/J has dimension 1, so J*** is not equal to J*.
		This is also an example where J is isometric to J, but J is not reflexive**.
	www.math.niu.edu /~rusin/known-math/98/reflexive (198 words)

	Reflexively But Not Unitarily Representable Topological Groups - Megrelishvili (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		M.G. Megrelishvili, Reflexively but not unitarily representable topological groups, submitted in Topology Proceedings, 1 th Turkish International Conference of Topology and Its Applications, August 2000.
		6 Uniform embeddings of metric spaces and of Banach spaces int..
		5 Additive subgroups of topological vector spaces (context) - Banasczyk - 1991
	citeseer.ist.psu.edu /492394.html (461 words)

	Denka Kutzarova
		On a class of Banach spaces (in Bulgarian), Proc.
		On equivalent translation invariant norms which are uniformly convex or uniformly differentiable in every direction in Köthe spaces (in Bulgarian), Proc.
		A nearly uniformly convex space which is not a (β)-space, Acta Univ. Carolinae - Math.
	www.math.uiuc.edu /~denka/denkapub.html (816 words)

	Art Bulletin, The: The self pictured: Manet, the mirror, and the occupation of realist painting
		It may be said, then, that the indeterminate space evoked by the mirror mode of looking is a reflexive space akin to that of self-portraiture.
		It may be possible, in fact, to discuss Manet's realism as taking place in a distinctly ecological space, that is, in a realm halfway between mimesis and semiosis, a space in which looking is an event of construing reality - natural or social - from a subjective prospect.
		In fact, the pairing of the male figure with the still life of the jug in each picture is nearly identical in conception.
	www.findarticles.com /p/articles/mi_m0422/is_1_80/ai_54073921/pg_8 (981 words)

	My space : citing (func)
		1991 R.M. Aron, B.J. Cole, T.W. Gamelin, "Spectra of algebras of analytic functions on a Banach space." J. Reine Angew.
		1993 C. Boyd, "Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces." Studia Math.
		1993 J.A. Jaramillo, A. Prieto, "Weak-polynomial convergence on a Banach space." Proc.
	www.tau.ac.il /~tsirel/Research/myspace/cit_func.html (364 words)

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