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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.
3
votes
2
answers
238
views
Polar decomposition of tensor product of operators in von Neumann algebra
If $T=V|T|\text { and } S=W|S|$ is the polar decomposition of $T$. Is it true that the polar decomposition of $T\otimes S$ is $T\otimes S=(V\otimes W)(|T| \otimes |S|)$. If $T$ and $S$ are self-adjoin …
2
votes
0
answers
134
views
On crossed product of L^{P} spaces
Let $M$ be a von Neumann algebra with faithful normal state $\varphi$, and $G$ be a group action on $M$ preserving $\varphi$. Then is it true
\begin{align*}
L^{p}(M\rtimes G, \varphi^{M\rtimes G})\co …
2
votes
1
answer
83
views
On existence of fixed point operator
Let $M$ be an infinite dimensional non-type $I$ factor, given $\xi$ in $\mathcal{H}$, does there exist a not identify operator $x$ in $M$ such that $x\xi=\xi$, I have tried with taking projection $P_{ …