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# Topic: Banach algebra

###### In the News (Fri 20 Apr 18)

 Station Information - Banach algebra The algebra of bounded real- or complex-valued functions defined on some set (with pointwise multiplication and the supremum norm) is a Banach algebra. The algebra of continuous real- or complex-valued functions on some compact space (again with pointwise operations and supremum norm) is a Banach algebra. The set of invertible elements in any unitary Banach algebra is an open set, and the inversion operation on this set is continuous, so that it forms a topological group under multiplication. www.stationinformation.com /encyclopedia/b/ba/banach_algebra.html   (550 words)

 Banach algebra   (Site not responding. Last check: 2007-10-21) The algebra of all bounded real- or complex-valued functions defined on some set (with pointwise multiplication and the supremum norm) is a unital Banach algebra. The algebra of all bounded continuous real- or complex-valued functions on some locally compact space (again with pointwise operations and supremum norm) is a Banach algebra. The algebra of all continuous linear operators on a Banach space E (with functional composition as multiplication and the operator norm as norm) is a unital Banach algebra. nba.servegame.org /en/Banach_algebra.htm   (671 words)

 Banach algebra: Definition and Links by Encyclopedian.com - All about Banach algebra   (Site not responding. Last check: 2007-10-21) A Banach algebra, in functional analysis, is an associative algebra over the real or complex numbers which at the same time is also a Banach space. The algebra of continuous real- or complex-valued functions on some compact space (again with pointwise operations and supremum norm). The algebra of all linear continuous operators on a Banach space (with functional composition as multiplication and the operator norm[?] as norm) www.encyclopedian.com /ba/Banach-algebra.html   (433 words)

 PlanetMath: Banach algebra Definition 2 A Banach *-algebra is a Banach algebra The algebra of bounded operators on a Banach space is a Banach algebra for the operator norm. This is version 7 of Banach algebra, born on 2002-08-23, modified 2005-06-22. planetmath.org /encyclopedia/BAlgebra3.html   (109 words)

 ALL COUNTEREXAMPLES   (Site not responding. Last check: 2007-10-21) A Banach algebra A that is a topological direct sum (as a Banach space) of a pair of its Banach subalgebras which are isometrically isomorphic to A. BA16.dvi 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 Banach algebra with an unbounded approximate identity. web.um.ac.ir /~moslehian/cfa/ALL.HTM   (1368 words)

 Exponential function   (Site not responding. Last check: 2007-10-21) It is easy to see, that the exponential function maps any line in the complex plane to a logarithmic spiral in the complex plane with the centre at 0, noting that the case of a line parallel with the real or imaginary axis maps to a line or circle. In the context of non-commutative Banach algebras, such as algebras of matrices or operators on Banach or Hilbert spaces, the exponential function is often considered as a function of a real argument: Similarly, since the Lie algebra M(n, R) of all square real matrices belongs to the Lie group of all invertible square matrices, the exponential function for square matrices is a special case of the Lie algebra exponential map. www.sciencedaily.com /encyclopedia/exponential_function   (715 words)

 [No title] Let A be a Banach algebra and k(A) the ``KÂ­theory space'' K 0 (A) x BGL(A), where GL(A) and BGL(A) have the usual topology and K 0 (A) the discrete topology. We write A(X) for the Banach algebra of continuous functions f : X zzc A' such that f(x) = f(x), the complex conjugate of f(x). Note that if the involution on X is trivial, A(X) is just the usual Banach algebra of continuous functions on X with values in A. On the other hand, if X is a space with 2 points which are switched by the involution, A(X) is canonically isomorphic to A'. hopf.math.purdue.edu /Karoubi/A_descent_theorem.txt   (836 words)

 [No title]   (Site not responding. Last check: 2007-10-21) The algebra of all continuous linear operators on a Banach space (with functional composition as multiplication and the operator norm as norm) is a Banach algeba. The continuous linear operators on a Hilbert space form a C-star-algebra and therefore a Banach algebra. (G) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy(g) = ∫ x(h) y(h www.informationgenius.com /encyclopedia/b/ba/banach_algebra.html   (542 words)

 [No title]   (Site not responding. Last check: 2007-10-21) Banach Algebra Structure and Amenability of a Class of Matrix Algebras with Applications/Gholam Hossein Esslamzadeh; Supervised by: A.T Lau. In this thesis we consider the structure and applications of a new class of matrix algebras that we call them ???-Munn algebras.Some functional analytic properties as well as the relations between certain members of this category and the algebra of compact operators on a separable Hilbert space are described. The topological center of the second dual of ???-Munn algebras are considered and they are fully described in terms of the algebras that they were based on. dbase.irandoc.ac.ir /00233/00233761.htm   (161 words)

 Harmonic Analysis, May/04 Banach algebras arising in abstract harmonic analysis, such as the measure algebra M(G) and the completely bounded multipliers of the Fourier algebra M_{cb} A_2(G). We show that when A is a C*-algebra, a Banach algebra generated by idempotents, a semisimple annihilator Banach algebra, or the group algebra of a SIN or a totally disconnected group, bounded approximately local derivations from A into X are derivations. Abstract: Representations of the measure algebra M(G) of a locally compact group G on spaces of operators on B(H) (itself the von Neumann algebra of bounded operators on a Hilbert space H) have been studied by Stormer, Ghahramani, Neufang, Smith and the presenter. www.math.uwo.ca /~milnes/HA04.htm   (2701 words)

 Mathematics Tasmania Colloquia Page for 1995 There is a natural coaction of Uq(d) on the Cuntz algebra Od, which is the natural generalization to the coalgebra setting of the canonical representation of the unitary matrix group U(d) as automorphisms of Od. It will be explained how Banach algebra techniques can be applied to approximation schemes such as, for example, projection methods and quadrature methods for integral equations. The theory of Hopf algebra actions on algebras unifies the theories of: actions of groups as automorphisms on algebras, group graded rings, and actions of Lie algebras as derivations on associative algebras. www.maths.utas.edu.au /HomePage/Coll95.html   (2075 words)

 Nat' Academies Press, Biographical Memoirs V.63 (1994) In addition to the usual theory of Banach spaces and linear transformations, Hille was able to organize into a unified whole the calculus of vector-valued functions, function theory for vector-valued functions, and the operational calculus. The theory of commutative Banach algebras is introduced early in the book and plays a major role in the chapters on spectral theory and holomorphic semi-groups. The influence of Yosida and, to some extent, Feller is quite evident; and of course I took advantage of my being coauthor by including my own results on extended classes of semi-groups (distinguished by their behavior at the origin) and their generating theorems, perturbation theory, the adjoint semi-group, the operational calculus, and spectral theory. www.nap.edu /openbook/0309049768/html/218.html   (3438 words)

 Affine Mappings Of Invertible Operators (ResearchIndex) The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra. citeseer.ist.psu.edu /48855.html   (289 words)

 Banach Algebras Which are a Direct Sum of Division Algebras Banach Algebras Which are a Direct Sum of Division Algebras A is a direct sum of a finite number of division Banach algebras. Departamento de Algebra, Geometria y Topologia, Universidad de Malaga, 29080 Malaga, Spain. pandora.nla.gov.au /pan/20621/20030824/anziamj.austms.org.au/JAMSA/V44/Part2/Lopez.html   (81 words)

 K-theory for the Banach algebra of operators on James spaces   (Site not responding. Last check: 2007-10-21) K-theory for the Banach algebra of operators on James spaces K-theory for the Banach algebra of operators on James's quasi-reflexive Banach spaces Keywords: Banach algebras, operators on Banach spaces, K-theory. www.math.ku.dk /~laustsen/abstractjamesktheory.html   (122 words)

 Atlas: Perturbations of nonassociative Banach algebras by Anar Dosiev   (Site not responding. Last check: 2007-10-21) For associative Banach algebras the problem is well known and serious advancements were done by B.E. Johnson, Perturbations of Banach algebras, Proc. (3) 34 (1977) 439-458, and I. Raeburn, J.L. Taylor, Hochschild cohomology and perturbations of Banach algebras, J. Roughly speaking, by differentiating the identities of a nonassocitive Banach algebra we are raising on the cohomology level. atlas-conferences.com /cgi-bin/abstract/cane-32   (154 words)

 Charles Read's webpage Paper Amenable and weakly amenable Banach algebras with compact multiplication, (this paper concerns a commutative radical Banach algebra with a bounded approximate identity of normalised powers). On a Frechet algebra, the separating subspace of a derivation from the algebra to itself may not lie inside the radical. Paper "The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces" (in TeX DVI format). www.amsta.leeds.ac.uk /%7Eread   (813 words)

 Questions on Automatic Continuity (ResearchIndex) We present a variety of open questions in automatic continuity theory, concentrating on homomorphisms between Banach algebras and derivations from a Banach algebra A into a Banach A-bimodule. Introduction In automatic continuity theory, we are concerned with conditions that imply that a linear map between Banach spaces (or more general topological linear spaces) is necessarily continuous. 3 Homomorphisms of commutative Banach algebras (context) - Bade, Curtis - 1960 citeseer.ist.psu.edu /62485.html   (531 words)

 Banach Algebra Resources International Conference on Banach Algebras and Cohomology - Newcastle (ICBACN) Banach Algebras and their Applications - Banach Algebras 2003 Banach Algebras and their Applications - Banach Algebras 2005 www.math.ualberta.ca /~runde/ba.html   (137 words)

 Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics) by Ronald G. Douglas [ISBN: 0387983775] - ...   (Site not responding. Last check: 2007-10-21) It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in operator theory and to provide the necessary background for them assuming only the standard senior-first year graduate courses in general topology, measure theory, and algebra. It really is an excellent book, but I wanted the author to discuss the Brown-Douglas-Fillmore K-theory of operator algebras and give an in-depth discussion of the invariant subspace conjecture. www.adultdvdmagic.com /isbn_0387983775.html   (447 words)

 Automatic continuity for Banach algebras (ResearchIndex) B from a Banach algebra A into a commutative, semisimple Banach algebra B is continuous. A closely related result is Johnson's uniqueness-of-norm-theorem: every semisimple Banach algebra has a unique complete algebra norm. There are non-semsimple, commutative Banach algebras which have a unique complete algebra norm. citeseer.ist.psu.edu /626229.html   (357 words)

 j.j.green's thesis   (Site not responding. Last check: 2007-10-21) We consider Banach algebras for which this convergence satisfies some conditions of uniformity, concentrating on two conditions: when this convergence is uniform on the unit ball (spectral uniformity) and when this uniformity holds merely on the topologically nilpotent elements of the unit ball (topologically bounded index). For topologically bounded index we prove a topological version of a theorem of Jacobson and use this to investigate semigroup algebras and algebras of operators on a Banach space. We study the injectivity of semigroup algebras, construct an injective Banach algebra which does not satisfy a polynomial identity and make some remarks on a question of Le Merdy. www.vindaloo.uklinux.net /jjg/thesis/thesis.html   (310 words)

 Research Page   (Site not responding. Last check: 2007-10-21) A classical example of a Banach algebra is to look at the algebra of operators on a Banach space, or ideals thereof. These are also classical examples of Banach spaces (in the case of C*-algebras, now having almost eclipsed the study of general Banach algebras). Banach spaces and their applications in Analysis -- Also known as Kaltonfest. www.maths.ox.ac.uk /~daws/maths/phd.html   (505 words)

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