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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

-1 votes
2 answers
622 views

Invariance of spectrum under conjugation

Let $T$ be a self-adjoint invertible operator on $\mathcal{H}$ with a continuous spectrum, means the spectral measure is nonatomic. For which class of invertible operators $V$( with continuous spectru …
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0 votes
0 answers
54 views

On cyclicity of a module

Let $A$ be a $\text{ von Neumann algebra }$, $\mathcal{H}$ is a cyclic $A$ module, $G$ be a finite group acting on $A$, is $\mathcal{H}$ cyclic module over fixed point subalgebra of the action? Furthe …
user136400's user avatar
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_{ …
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0 votes
0 answers
127 views

On examples of action of C-star simple group on von Neumann algebra

Can there exist a faithful action of a $C^{*}$-simple group $G$ on a von Neumann algebra $(M,\varphi)$ equipped with faithful normal state $\varphi$ such that action preserves the state $\varphi$ and …
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