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15
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Show that $T$ is compact if and only if $\lim_{n \rightarrow \infty} |\alpha_n|=0$

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#functional-analysis #compact-operators
124
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Exercise on eigenvalues of an Hilbert-Schimdt operator

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#functional-analysis #eigenvalues-eigenvectors #compact-operators #integral-equations
55
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The spectrum of $S$ is a countable set?

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#functional-analysis #operator-theory #compact-operators
69
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singular values of infinite direct sum of operators

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#eigenvalues-eigenvectors #operator-theory #compact-operators #singular-values
124
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About proof of 8.3-5 in Kreyszig's Functional Analysis

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#functional-analysis #compact-operators
41
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Calculating a dimension of a kernel of a semi-Fredholm composition operator

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#banach-spaces #compact-operators
144
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If $\dim H=\infty$, does there always exist a positive compact operator $T$ with infinite rank and $\|T\|\leq1$?

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#functional-analysis #operator-theory #hilbert-spaces #operator-algebras #compact-operators
147
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Why is this representation of $C^*\!$-algebras irreducible?

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#functional-analysis #operator-theory #c-star-algebras #compact-operators
86
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Prove lim$_{n \rightarrow \infty}c_n=0$

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#functional-analysis #compact-operators
112
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Eigenvalues of an infinite block upper triangular matrix

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#compact-operators #infinite-matrices
247
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Every *-isometric isomorphism of $B(\mathcal{H})$ keep compact operators?

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#functional-analysis #operator-theory #operator-algebras #compact-operators
38
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$\text{Image}(I−K)(V) = \{x−Kx; x \in V \text{closed} \}$ is a closed subspace of hilbert space $H$.

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#functional-analysis #analysis #hilbert-spaces #solution-verification #compact-operators
37
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If $A=\sum_{i\in I}\lambda_ie_i\otimes e_i$ is compact, self-adjoint and nonnegative, then $\left\|A\right\|=\lambda_1$

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#functional-analysis #operator-theory #hilbert-spaces #spectral-theory #compact-operators
221
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Example for a polynomially compact operator

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#functional-analysis #operator-theory #examples-counterexamples #normed-spaces #compact-operators
51
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Is it possible to find a basis for a non-compact operator?

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#functional-analysis #operator-theory #compact-operators

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