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Results tagged with c-star-algebras
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user 20746
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
2
answers
1k
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Polar decomposition in C*-algebras
A very nice feature of W*-algebras is the following:
once you have an element $a$ of a W*-algebra $M$, and $a=u|a|$ (the polar decomposition), then $u\in M$.
It seems that it carries over to AW*-alg …
- 2,821
3
votes
1
answer
498
views
When an AW*-algebra is a W*-algebra
In a very old book of Kaplansky "Rings of operators", on p. 123 one can find the following sentence:
It is a standing conjecture that an AW${}^\ast$-algebra is W${}^\ast$ if its center is W${}^\ast$. …
- 42.8k
13
votes
2
answers
963
views
C*-algebras with bizzarre structure of projections
This is probably well-known to the experts but I could not find any answer neither in my head nor in the literature: Is there a (unital) C*-algebra such that its projections do not form a lattice (und …
- 2,049