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Results tagged with c-star-algebras
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user 100607
A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
5
votes
Classification of $C^*$ algebras whose all non scalar elements have disconnected spectrum
The following might be useful. For a C*-algebra $A$, the following statements are equivalent:
1) $A$ is scattered;
2) the spectrum of any self-adjoint element in $A$ is countable
3) all maximal com …
8
votes
Accepted
Can an AW*-algebra be recovered from its lattice of projections?
Yes, this follows from Theorem 4.2 in Dye's Theorem and Gleason's Theorem for AW*-algebras by Jan Hamhalter.
Link: https://arxiv.org/abs/1408.4597
Here the statement is: given an AW*-algebra $A$ with …