Tagged Questions

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Conditional expectation onto maximal abelian subalgebras

If you take a von Neumann algebra $M$ and any its maximal abelian subalgebra (masa) $D$, then there is a norm-one projection from $M$ onto $D$ (conditional expectation). The same is true if you take ...
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Dual of injective tensor norm is not projective tensor norm

Let $A$, $B$ are two Banach space, on the algebraic tensor space $A$ $\odot$ $B$, we can define the projection（maximal） tensor norm $\gamma$ and injective（minimal） tensor norm $\lambda$. For the ...
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Questions about $B(H)$ and $B(H)/K(H)$ as Banach space

I am trying to investigate the relation between Uniformly Convexity and existence of Schauder Basis for a Banach space. I read in a Handbook article that $B(H)$ (the algebra of all bounded operators ...
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Smallness/ Rigidity of $\kappa(\mathcal{H})$ without using minimal projections?

Let $\mathcal{H}$ be a Hilbert space and $\kappa(\mathcal{H})$ the $C^*$-algebra of compact operators on $\mathcal{H}$. By smallness/ rigidity of $\kappa(\mathcal{H})$ I am referring to the following ...
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I have basically finished my grad school applications and have some time at hand. I want to start reading some classic papers in Operator Theory so as to breathe more culture here. I have read some ...
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An explicit example of an invariant halfspace of the unilateral shift?

In a recent talk, A. Popov stated the following fact The unilateral shift on $\ell^2$ has invariant halfspaces. Halfspaces are closed subspaces whose dimension and codimension are both infinite. ...
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An upper bound for $\|(\lambda-A)^{-1}\|$?

Let $A$ be a k-by-k matrix and $\sigma(A)$ its spectrum, or the collection of eigenvalues of $A$. If we know $\lambda\notin\sigma(A)$, then $\lambda$ is at a positive distance to all points in the ...
How does $\sigma(T)$ change with respect to $T$?
Consider $\sigma$ as a mapping which maps $T\in\mathcal{L}(X)$ to $\sigma(T)$, the spectrum of $T$, a compact set in the complex plane. I wonder whether there is some result concerning how ...