List questions from compact-operators

Published on 25 Mar 2026 - 1:15

441

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Why is this compact operator a Fredholm operator?

Published on 02 Jun 2018 - 16:57

215

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Polynomial and operator in Hilbert space

Published on 06 Jun 2018 - 17:42

50

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

Published on 10 Jun 2018 - 14:49

88

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Compactness of operators and norming sets

Published on 13 Jun 2018 - 1:20

171

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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 16 Jun 2018 - 2:22

49

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Optimal conditions for Schrödinger semigroup to be Hilbert-Schmidt

Published on 20 Jun 2018 - 19:59

1.5k

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Does each compact operator have a non–zero eigenvector?

Published on 21 Jun 2018 - 4:08

360

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Compactness criterion for operator between reflexive Banach spaces

Published on 23 Mar 2026 - 1:22

56

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Adjoint of $T$, infinite dimensional space

Published on 05 Jul 2018 - 5:59

643

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

Published on 05 Jul 2018 - 16:53

92

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

Published on 08 Jul 2018 - 2:49

238

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

Published on 24 Mar 2026 - 22:08

128

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

Published on 25 Mar 2026 - 6:10

68

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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 21 Jul 2018 - 0:52

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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