# Questions tagged [operator-algebras]

The subject of operator algebras is primarily C*-algebras and von Neumann algebras, and associated topics. It also includes more general algebras of operators on Hilbert space, and may include algebras of operators on other topological vector spaces. It is related to but distinct from the subjects of the tags (banach-algebras), (c-star-algebras), (von-neumann-algebras), and (operator-theory).

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### If we found a norm for a subalgebra of a C*algebra, is it in fact equivalent to the original norm?

This is from the textbook "An introduction to K-theory for C*alebgra" : So I don't have a question about the problem itself but am more interested in the fact that we can define the norm ...
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### What is odd element of C*-algebra? [closed]

I cannot nowhere find a definition of an odd/even element of C*-algebra. Can someone write it here?
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### Extension of slice map to WOT closure

Given Hilbert spaces $H_1,H_2$ and a functional in the predual $\psi\in B(H_1)_*$ we may consider the slice map $S:B(H_1)\otimes B(H_2)\to B(H_2)$ defined on the spatial tensor product given by ...
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### Compression map is an isomorphism from $pB(H)p$ to $B(K)$ via $u \to u_K$

I was reading a note on Von Neumann Algebra, and I am not able to understand this phrase as: Let $K$ be a closed vector subspace of a Hilbert space $H$ and let $p$ be the projection of $H$ onto $K$. ...
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### Minimal tensor product of $B(H)$ and $C(G)$

Let $H$ be a finite dimensional vector space, and $G$ be a compact group. Let $B(H)$ be the bounded operators on $H$, let $C(G)$ be the complex valued continuous functions on $G$, and let $C(G;B(H))$ ...
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### When is a group von Neumann algebra a factor?

It is well-known that a von Neumann algebra (on a separable Hilbert space) can be written as a direct integrals of factors, i.e., von Neumann algebras with center $\mathbb C I$. As such, factors play ...
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I have seen it stated that for an open subset $Y\subseteq X$ such that $X$ is a compact Hausdorff space we get an identification of the $C^*$-algebras : $C(X\setminus Y)\cong C(X)/C_0(Y)$. I suppose ...