List questions from compact-operators

310

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Compact operator $L:\ell^2\to\ell^2$ with $\Vert L\Vert=1$ such that $\Vert L(x)\Vert<\Vert x\Vert$ for all $x$

Published on 14 Apr 2026 - 19:26

193

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Compact operator on $L_2([0,1],m)$

Published on 13 Apr 2026 - 6:41

148

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Compact open operator between Banach spaces

Published on 10 May 2026 - 15:41

173

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Compact embedding of the domain and compact inverse

Published on 17 Apr 2026 - 4:23

63

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Norm and compactness of the Operator $(Tu)(x)=\alpha(x)u'(x), u\in Y, x\in I$

Published on 16 Apr 2026 - 18:41

222

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Show that this operator is not compact using Arzela-Ascoli

Published on 09 Apr 2026 - 11:59

446

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Compactness of an integral operator from $L^2$ to $L^2$

Published on 09 Apr 2026 - 8:16

239

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Show compactness of an operator

Published on 10 May 2026 - 23:52

122

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Question on Compact operators: Suitable definition of a sequence of compact operators

Published on 10 Apr 2026 - 16:12

590

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Help understanding proof that Hilbert-Schmidt operators are compact

Published on 11 Apr 2026 - 6:48

55

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Source for a particular proof of the spectral theorem.

Published on 10 May 2026 - 17:37

1.3k

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Linear operator is compact if and only if its adjoint is compact

Published on 11 May 2026 - 4:15

63

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$\tilde{T} : X/X_0 \to Y $ is also compact

Published on 15 Apr 2026 - 19:02

60

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$T :N \to N_1$ is compact iff closure of $T(S)$ is compact $\forall S$ bounded subset of $N$

Published on 13 Apr 2026 - 15:45

85

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Spectral theory: Operator compact implies existence of convergent subsequence

Published on 10 Apr 2026 - 10:19

List Question

Compact operator $L:\ell^2\to\ell^2$ with $\Vert L\Vert=1$ such that $\Vert L(x)\Vert<\Vert x\Vert$ for all $x$

Compact operator on $L_2([0,1],m)$

Compact open operator between Banach spaces

Compact embedding of the domain and compact inverse

Norm and compactness of the Operator $(Tu)(x)=\alpha(x)u'(x), u\in Y, x\in I$

Show that this operator is not compact using Arzela-Ascoli

Compactness of an integral operator from $L^2$ to $L^2$

Show compactness of an operator

Question on Compact operators: Suitable definition of a sequence of compact operators

Help understanding proof that Hilbert-Schmidt operators are compact

Source for a particular proof of the spectral theorem.

Linear operator is compact if and only if its adjoint is compact

$\tilde{T} : X/X_0 \to Y $ is also compact

$T :N \to N_1$ is compact iff closure of $T(S)$ is compact $\forall S$ bounded subset of $N$

Spectral theory: Operator compact implies existence of convergent subsequence

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