A commutative Banach algebra is a Banach algebra A with the property that ab = ba for all a, b ∈ A Examples and are of commutative. Banach. Of course, if A is a normed algebra, then the norm induces a metric on A which Similarly weak star topology on A∗ is generated by the sets. *-SJbalgebra A of B (H) which is closed in tIE nonn tOIDlogy is a C*-algebra. E.g.: . A C*-algebra A is unital if A has a unit 1 A i otherwise, A is nonunital. I.

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The involution is given by the conjugate transpose.

Please help improve this article by adding citations to reliable sources. In the latter case, we can use the fact that the structure of these is completely determined by the Gelfand isomorphism. This article needs additional citations for verification.

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K H is a two-sided closed ideal of B H. Kribs, and Raymond Laflamme. February Learn how and when to remove this template message.


Subsequently, John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators. For separable Hilbert spaces, it is the unique ideal. In the language of K-theorythis vector is the positive cone of the K 0 group of A.

From Wikipedia, the free encyclopedia. This characterization is one of the motivations for the noncommutative topology and noncommutative geometry programs.


This line of research began with Werner Heisenberg ‘s matrix mechanics and in algebr more mathematically developed form with Pascual Jordan around In fact it is sufficient to consider only factor representations, i.

Let H be a separable infinite-dimensional Hilbert space.

Segal in to describe norm-closed subalgebras of B Hnamely, the space algebar bounded operators on some Hilbert space H. Unsourced material may be challenged and removed. Elements of this cone are called non-negative or sometimes positiveeven though this terminology conflicts with its use for elements of R. Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point.


C^*-Algebra — from Wolfram MathWorld

More generally, one can consider finite direct sums of matrix algebras. Such functions exist by the Tietze extension theorem which applies to locally compact Hausdorff spaces. This page was last edited on 27 Julyat Though K H does not have an algehra element, a sequential approximate identity for K H can be developed.

Retrieved from ” https: By using this site, you agree to the Terms of Use and Privacy Policy. The involution is pointwise conjugation. Algebrra needing additional references from February All articles needing additional references Wikipedia articles needing clarification from August They are required to be closed in the weak operator topologywhich is weaker than the norm topology. Let X be a locally compact Hausdorff space.