List questions from compact-operators

Published on 11 Apr 2026 - 23:00

171

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Submultiplicative aspect of L^2 norm. Should I use a different one? Cauchy Schwartz

Published on 11 Apr 2026 - 17:12

257

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Does there exist an infinite dimensional compact operator on any infinite dimensional Banach space?

Published on 13 Apr 2026 - 7:53

151

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Show that the integral-operator compact?

Published on 10 Apr 2026 - 18:23

349

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If an operator in $X$ with compact resolvent is bounded, $X$ must be finite dimensional.

Published on 11 Apr 2026 - 11:51

180

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Expressing an operator as a sum of the identity and a compact operator

Published on 23 Apr 2026 - 18:20

35

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Is there such subsequence in $L^2(\Bbb{R}^2)$.

Published on 24 Mar 2026 - 22:08

106

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Is it possible to obtain an expression for the spectrum of a compact embedding operator? E.g. for $I:H^1([0,1])\to L^1([0,1])$?

Published on 11 Apr 2026 - 2:46

359

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polar decomposition of compact operators

Published on 10 May 2026 - 15:22

558

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For which n differential operator $C^{(n)}[0, 1] \rightarrow C[0,1]$ is compact

Published on 16 Apr 2026 - 11:00

257

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Compact embedding between $H^{m+1}(\Omega)$ and $H^{m}(\Omega)$ for $\Omega$ bounded

Published on 17 Apr 2026 - 10:11

82

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Relationship between eigenvalues of compact operators $A$ and $(A+A^*)/2$

Published on 17 Apr 2026 - 2:52

75

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If $A$ is a compact operator, then the rank of $A^*A$ is equal to the rank of $A$.

Published on 14 Apr 2026 - 4:24

1.3k

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Fredholm operator of index 0

Published on 14 Apr 2026 - 22:54

130

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Compact or noncompact operator?

Published on 11 Apr 2026 - 7:48

List Question

$T$ is compact iff $\langle Te_i,e_j\rangle\to 0$ as $i,j\to\infty$

Submultiplicative aspect of L^2 norm. Should I use a different one? Cauchy Schwartz

Does there exist an infinite dimensional compact operator on any infinite dimensional Banach space?

Show that the integral-operator compact?

If an operator in $X$ with compact resolvent is bounded, $X$ must be finite dimensional.

Expressing an operator as a sum of the identity and a compact operator

Is there such subsequence in $L^2(\Bbb{R}^2)$.

Is it possible to obtain an expression for the spectrum of a compact embedding operator? E.g. for $I:H^1([0,1])\to L^1([0,1])$?

polar decomposition of compact operators

For which n differential operator $C^{(n)}[0, 1] \rightarrow C[0,1]$ is compact

Compact embedding between $H^{m+1}(\Omega)$ and $H^{m}(\Omega)$ for $\Omega$ bounded

Relationship between eigenvalues of compact operators $A$ and $(A+A^*)/2$

If $A$ is a compact operator, then the rank of $A^*A$ is equal to the rank of $A$.

Fredholm operator of index 0

Compact or noncompact operator?

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