# Tagged Questions

Operator theory is the branch of functional analysis that focuses on bounded linear operators, but it includes closed operators and nonlinear operators. Operator theory is also concerned with the study of algebras of operators.

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### Are $X'\otimes Y$ and $\mathfrak L(X,Y)$ isomorphic?

Let $\mathbb F\in\left\{\mathbb C,\mathbb R\right\}$ $X$ and $Y$ be normed $\mathbb F$-vector spaces $X'$ be the topological dual space of $X$ $\mathfrak L(X,Y)$ be the set of bounded, linear ...
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### What does 'mode' mean in this context?

The spectrum of an operator $\mathcal{L}$ is the disjoint union of two sets: the point spectrum that consists of all isolated eigenvalues with finite multiplicity and its complement, which we call the ...
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### functional analysis and operator theory

If the nonlinear operator N defined on R^n into itself is contraction mapping then how to show I+N is onto operator? where I is identity operator.
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### $Tf = xf(x)$ is not compact in $L^2([0,1])$

I want to prove, in a rather elementary way, that $Tf = xf(x)$ is not compact in $L^2([0,1])$. I cannot find the appropriate bounded sequence whose image has no Cauchy sub-sequences. I have tried ...
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### subset of pure states with norm condition already dense

I struggle to proof the following statement: Let $Y\subseteq P\left(B\right)$ a subset of pure states on a $C^*$-Algebra $B$ such that for every $b\in B$ there exists a $\varphi \in P \left(B\right)$ ...