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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In fact it is sufficient to consider only factor representations, i. More generally, one can consider finite direct sums of matrix algebras. This characterization is one of the motivations for the noncommutative topology and noncommutative geometry programs. K H is a two-sided closed ideal of B H.

Unsourced material algevra be challenged alebra removed. Segal in to describe norm-closed subalgebras of B Hnamely, the space of bounded operators on some Hilbert space H.


C-star-algebra in nLab

In the latter case, we can use the fact that the structure of these is completely determined by the Gelfand isomorphism. From Wikipedia, the free encyclopedia.

The involution is pointwise conjugation. The involution is sctar by the conjugate transpose. Please help improve this article by adding citations to reliable sources.

C^*-Algebra — from Wolfram MathWorld

Volume 2, Number 5, p. This algebga was last edited on 27 Julyat Such functions exist by the Tietze extension theorem which applies to locally compact Hausdorff spaces.

February Learn how and when to remove this template message. Kribs, and Raymond Laflamme.


This article needs additional citations for verification. Articles needing additional references from February All articles needing additional references Wikipedia articles needing clarification from August Elements of this cone are called non-negative or sometimes positiveeven though this terminology conflicts with its use for elements of R. Retrieved from ” https: For separable Hilbert spaces, it is the algegra ideal.


Let X be a locally compact Hausdorff space. This line of research began with Werner Heisenberg ‘s matrix mechanics and in a more mathematically developed form with Pascual Jordan around Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point. Views Read Edit View history.

Subsequently, John von Neumann attempted alvebra establish a general framework for these algebras which culminated in a series of papers on rings of operators. By using this site, you agree to the Terms of Use and Privacy Policy. Though K H does not have an identity element, a sequential approximate identity for K H can be developed.

They are required to be closed in the weak operator topologywhich is weaker than the norm topology. Let H be a separable infinite-dimensional Hilbert space. In the language of K-theorythis vector is the positive cone of the K 0 group of A.

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