List questions from compact-operators

Published on 10 May 2026 - 14:53

444

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Why is this compact operator a Fredholm operator?

Published on 08 Apr 2026 - 16:50

218

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Polynomial and operator in Hilbert space

Published on 09 Apr 2026 - 11:12

53

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Extending Fredholm Alternative on Banach Spaces to $\mathbb{R}$

Published on 09 Apr 2026 - 17:14

91

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Compactness of operators and norming sets

Published on 12 Apr 2026 - 11:00

174

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Let $E$ Banach space, $\dim E = \infty$ and $T: E \longrightarrow E$ a linear isometry. Show that $T$ is not compact.

Published on 13 Apr 2026 - 11:05

52

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Optimal conditions for Schrödinger semigroup to be Hilbert-Schmidt

Published on 12 Apr 2026 - 23:22

1.5k

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Does each compact operator have a non–zero eigenvector?

Published on 10 Apr 2026 - 14:00

365

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Compactness criterion for operator between reflexive Banach spaces

Published on 28 Apr 2026 - 18:52

59

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Adjoint of $T$, infinite dimensional space

Published on 15 Apr 2026 - 4:09

646

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Prove that $Tf(x)=\int^{1-x}_0 f(t) \, dt$ is compact and compute its spectrum.

Published on 16 Apr 2026 - 15:08

95

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Is there a compact operator in $\ell^2$ satisying these properties?

Published on 10 Apr 2026 - 18:22

240

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What is known about the reciprocal $1/f$ of a holomorphic Banach-valued function $f$?

Published on 29 Apr 2026 - 12:54

130

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Compact operator on invariant subspace (not necessarily closed) is compact

Published on 10 May 2026 - 14:25

71

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Prove that there exists sequence $(u_n)$ in $E$ such that $\| u_n \|_E = 1$ and $\| Tu_n\|_F \rightarrow 0.$

Published on 16 Apr 2026 - 11:07

List Question

Show that a compact operator is bounded

Why is this compact operator a Fredholm operator?

Polynomial and operator in Hilbert space

Extending Fredholm Alternative on Banach Spaces to $\mathbb{R}$

Compactness of operators and norming sets

Let $E$ Banach space, $\dim E = \infty$ and $T: E \longrightarrow E$ a linear isometry. Show that $T$ is not compact.

Optimal conditions for Schrödinger semigroup to be Hilbert-Schmidt

Does each compact operator have a non–zero eigenvector?

Compactness criterion for operator between reflexive Banach spaces

Adjoint of $T$, infinite dimensional space

Prove that $Tf(x)=\int^{1-x}_0 f(t) \, dt$ is compact and compute its spectrum.

Is there a compact operator in $\ell^2$ satisying these properties?

What is known about the reciprocal $1/f$ of a holomorphic Banach-valued function $f$?

Compact operator on invariant subspace (not necessarily closed) is compact

Prove that there exists sequence $(u_n)$ in $E$ such that $\| u_n \|_E = 1$ and $\| Tu_n\|_F \rightarrow 0.$

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