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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
4
votes
1
answer
198
views
Does noncommutative Lp-convergence respect orderings?
Let $M$ be a von Neumann algebra and $\tau$ a faithful (semi-finite?) normal trace on $M$; as is standard, the $L^p$-norm is defined as $||u||_p=\tau(|u|^p)^{1/p}$. Let $\{u_i\}_{i=1}^\infty$ be a seq …
5
votes
0
answers
154
views
When is an inner derivation a Fredholm operator?
Let $\mathcal{B}(H)$ denote the algebra of bounded operators on a Hilbert space $H$. I'm interested in inner derivations acting on the Schatten ideals $L^p\subseteq\mathcal{B}(H)$ (defined by operator …
6
votes
1
answer
232
views
Noncommutative Poincaré inequalities
This is a question on how (or if) people in the community think about the Poincaré inequality in noncommutative geometry. In geometry, the Poincaré inequality (when it exists) gives a bound on a funct …
6
votes
1
answer
755
views
Example of an infinite dimensional reflexive Banach algebra
If a $C^\ast$-algebra is reflexive (as a Banach space) then it is finite dimensional. Can anyone provide (or give a reference to) a nice example of an infinite dimensional non-commutative Banach algeb …
4
votes
2
answers
640
views
Lower bounds for norms of commutators
For various reasons I became interested in bounds on the norm of commutators of operators. For instance, if $B(H)$ is the algebra of bounded operators on a Hilbert space, one may ask for a lower bound …