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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C^*-Algebra — from Wolfram MathWorld

In fact it is sufficient to consider only factor representations, i. Articles needing additional references from February All articles needing additional references Wikipedia articles needing clarification from August This characterization is one of the motivations for the noncommutative topology and noncommutative geometry programs. This article needs additional citations for verification.

K H is a two-sided closed ideal of B H. In the latter case, we algebea use the fact that the structure of these is completely determined by the Gelfand isomorphism. Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point.


Please help improve this article by adding citations to reliable sources. This page was last edited on 27 Julyat For separable Hilbert spaces, it is the unique ideal. By using this site, you agree to the Terms of Use and Privacy Policy.


Kribs, and Raymond Laflamme. Volume 2, Number 5, p. This line of research began with Werner Heisenberg ‘s matrix mechanics and in a algegra mathematically developed form with Pascual Jordan around Elements of this cone are called non-negative or sometimes positiveeven though this terminology conflicts with its use for elements of R.

Such functions exist by the Tietze extension theorem which applies to locally compact Hausdorff spaces. In the language of K-theorythis vector is the positive cone of the K 0 group of A. Let X be a locally compact Hausdorff space.

Though K H does not have an cstaf element, a sequential approximate identity for K H can be developed. Subsequently, John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators.


Let H be a separable infinite-dimensional Hilbert space. Views Read Edit View history.

C-star-algebra in nLab

Segal in to describe norm-closed subalgebras of B Hnamely, the space of bounded operators on some Hilbert space H. They are required to be closed in the weak operator topologywhich is weaker than the norm topology. The involution is given by the conjugate transpose. From Wikipedia, xstar free encyclopedia.


More generally, one can consider finite direct sums of matrix algebras. Retrieved from ” https: The involution is pointwise conjugation. February Learn how and when to remove this template algebar.