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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Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point. The involution qlgebra pointwise conjugation. More generally, one can consider finite direct sums of matrix algebras. Elements of this cone are called non-negative or sometimes positiveeven though this terminology conflicts with its use for elements of R.
Unsourced material may be challenged and removed. Let H be a separable infinite-dimensional Hilbert space. In fact it is sufficient to consider only factor representations, i.
For separable Hilbert spaces, it is the unique ideal. Though K H does not have an identity element, a sequential approximate identity for K H can be developed. February Learn how and when to remove this template message.
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This characterization is one of the motivations for the noncommutative topology and noncommutative geometry programs. Let X be a locally compact Hausdorff space.
C^*-Algebra — from Wolfram MathWorld
This line of research began with Werner Heisenberg ‘s matrix mechanics and in a more mathematically developed form with Pascual Jordan around lagebra The involution is given by the conjugate transpose. Subsequently, John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators.
K H is a two-sided closed ideal of B H. Segal in to algebga norm-closed subalgebras of B Hnamely, the space of bounded operators on some Hilbert space H. Volume 2, Number 5, p.
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Articles needing additional references from February All articles needing additional references Wikipedia articles needing clarification from August In the latter case, we can use the fact that the structure of these is completely determined by the Gelfand isomorphism.
They are required to be closed in the weak operator topologywhich is weaker than the norm topology. Such functions exist by the Tietze extension theorem which applies to locally compact Hausdorff spaces.
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