Question

Proving an operator operator is compact on $L^p$, using Kolmogorov's theorem

score 132 · Answer 1 · 2026-03-26 22:13:40

132

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Proving an operator operator is compact on $L^p$, using Kolmogorov's theorem

Published on 26 Mar 2026 - 22:13

score 137 · Answer 2 · 2026-03-26 22:13:18

137

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How to show That T is not compact

Published on 26 Mar 2026 - 22:13

score 1.2k · Answer 3 · 2026-03-26 22:15:11

1.2k

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A compact operator that is the limit of finite rank operators

Published on 26 Mar 2026 - 22:15

score 60 · Answer 4 · 2026-03-26 22:13:05

60

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Compact operators on $L^2([a,b])$: Are the dimensions of eigenspaces the same on dense subspaces?

Published on 26 Mar 2026 - 22:13

score 602 · Answer 5 · 2026-03-26 22:15:15

602

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How to show that finite rank operator on Banach space is compact

Published on 26 Mar 2026 - 22:15

score 449 · Answer 6 · 2026-03-27 00:02:52

449

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Finite rank operator are dense in trace class with trace class norm .

Published on 27 Mar 2026 - 0:02

score 892 · Answer 7 · 2026-03-26 22:14:02

892

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spectrum of an operator and its point and continuous spectrum

Published on 26 Mar 2026 - 22:14

score 102 · Answer 8 · 2026-03-26 22:18:10

102

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If $T$ is compact there is some $n$ such that $\operatorname{range}(T-\alpha I)^n=\operatorname{range}(T-\alpha I)^{n+1}$

Published on 26 Mar 2026 - 22:18

score 718 · Answer 9 · 2026-03-27 00:02:41

718

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Operators that improve strong convergence to norm convergence?

Published on 27 Mar 2026 - 0:02

score 70 · Answer 10 · 2026-05-11 04:19:26

70

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Continuous group of automorphisms of $K(H)$

Published on 11 May 2026 - 4:19

score 84 · Answer 11 · 2026-03-26 22:19:50

84

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Show that $T$ is compact

Published on 26 Mar 2026 - 22:19

score 565 · Answer 12 · 2026-05-11 06:28:22

565

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Equivalence between closed range + finite dimensional kernel, and a statement about sequences.

Published on 11 May 2026 - 6:28

score 49 · Answer 13 · 2026-03-26 22:14:10

49

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Prove the compactness of an operator in a Hilbert space

Published on 26 Mar 2026 - 22:14

score 428 · Answer 14 · 2026-03-27 00:10:06

428

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Is the operator $T:C([0,1])\to C([0,1])$ defined by $(Tf)(x)=\int_0^x h(y)f(y) dy$ where $h\in L^2([0,1])$ compact?

Published on 27 Mar 2026 - 0:10

score 163 · Answer 15 · 2026-03-26 22:19:50

163

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$Tx=\sum_{k=0}^{\infty}\lambda_k(x,e_k)e_k$ bounded and compact iff $\lambda_k\to 0$

Published on 26 Mar 2026 - 22:19

List Question

Proving an operator operator is compact on $L^p$, using Kolmogorov's theorem

How to show That T is not compact

A compact operator that is the limit of finite rank operators

Compact operators on $L^2([a,b])$: Are the dimensions of eigenspaces the same on dense subspaces?

How to show that finite rank operator on Banach space is compact

Finite rank operator are dense in trace class with trace class norm .

spectrum of an operator and its point and continuous spectrum

If $T$ is compact there is some $n$ such that $\operatorname{range}(T-\alpha I)^n=\operatorname{range}(T-\alpha I)^{n+1}$

Operators that improve strong convergence to norm convergence?

Continuous group of automorphisms of $K(H)$

Show that $T$ is compact

Equivalence between closed range + finite dimensional kernel, and a statement about sequences.

Prove the compactness of an operator in a Hilbert space

Is the operator $T:C([0,1])\to C([0,1])$ defined by $(Tf)(x)=\int_0^x h(y)f(y) dy$ where $h\in L^2([0,1])$ compact?

$Tx=\sum_{k=0}^{\infty}\lambda_k(x,e_k)e_k$ bounded and compact iff $\lambda_k\to 0$

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