Question

Multiplication operator is compact in $L_2[0,1]$

score 156 · Answer 1 · 2022-07-20 08:48:07

156

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Multiplication operator is compact in $L_2[0,1]$

Published on 20 Jul 2022 - 8:48

score 57 · Answer 2 · 2022-07-20 17:45:58

57

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Characterization of compact operators in hilbert spaces

Published on 20 Jul 2022 - 17:45

score 58 · Answer 3 · 2022-07-21 02:46:02

58

Views

Show that the sum operator is not compact

Published on 21 Jul 2022 - 2:46

score 42 · Answer 4 · 2022-07-26 00:51:05

42

Views

Analysis of a operator in $L_2 [0,1]$

Published on 26 Jul 2022 - 0:51

score 410 · Answer 5 · 2026-03-27 14:50:39

410

Views

About kernel of compact self-adjoint operators and separable Hilbert spaces

Published on 27 Mar 2026 - 14:50

score 82 · Answer 6 · 2026-02-23 12:01:10

82

Views

Krein-Rutman theorem for kernel operators

Published on 23 Feb 2026 - 12:01

score 309 · Answer 7 · 2026-02-24 01:04:25

309

Views

Prove that the integral operator $T:\mathcal{C}([0,1]) \to \mathcal{C}([0,1])$ is compact

Published on 24 Feb 2026 - 1:04

score 68 · Answer 8 · 2022-07-28 08:59:48

68

Views

Prove that the operator $T:l^{\infty}(\mathbb{R}) \to l^{\infty}(\mathbb{R})$ is compact

Published on 28 Jul 2022 - 8:59

score 54 · Answer 9 · 2022-08-08 11:59:22

54

Views

The ideal generated by the discrete multiplication operators is closed

Published on 08 Aug 2022 - 11:59

score 116 · Answer 10 · 2022-08-08 17:06:20

116

Views

Is product of two compact operator on a Hilbert space is also compact?

Published on 08 Aug 2022 - 17:06

score 42 · Answer 11 · 2022-08-19 11:35:48

42

Views

$T = \operatorname{diag}\{p_1, p_2, \ldots\} \oplus A$ with $p_j \geqslant 0$ and $A \leqslant 0$

Published on 19 Aug 2022 - 11:35

score 224 · Answer 12 · 2022-08-20 11:34:36

224

Views

Prove that certain integral operator on $L^1[0,\infty)$ is compact

Published on 20 Aug 2022 - 11:34

score 54 · Answer 13 · 2026-03-27 14:51:39

54

Views

Let $H$ and $V$ be bounded self-adjoint operators. If $V$ is compact then $E_{H+V}(J)-E_{H}(J)$ is a compact operator.

Published on 27 Mar 2026 - 14:51

score 24 · Answer 14 · 2022-08-30 03:09:35

24

Views

(Solved) Example: $u$ not a weak limit point but $Ku$ a strong limit point, where $K$ a compact operator on Hilbert space.

Published on 30 Aug 2022 - 3:09

score 134 · Answer 15 · 2022-09-15 11:54:17

134

Views

If $T_{1}$ is dominated by $T_{2}$ and $T_{2}$ is a compact operator, can we deduce that $T_{1}$ is a compact operator?

Published on 15 Sep 2022 - 11:54

List Question

Multiplication operator is compact in $L_2[0,1]$

Characterization of compact operators in hilbert spaces

Show that the sum operator is not compact

Analysis of a operator in $L_2 [0,1]$

About kernel of compact self-adjoint operators and separable Hilbert spaces

Krein-Rutman theorem for kernel operators

Prove that the integral operator $T:\mathcal{C}([0,1]) \to \mathcal{C}([0,1])$ is compact

Prove that the operator $T:l^{\infty}(\mathbb{R}) \to l^{\infty}(\mathbb{R})$ is compact

The ideal generated by the discrete multiplication operators is closed

Is product of two compact operator on a Hilbert space is also compact?

$T = \operatorname{diag}\{p_1, p_2, \ldots\} \oplus A$ with $p_j \geqslant 0$ and $A \leqslant 0$

Prove that certain integral operator on $L^1[0,\infty)$ is compact

Let $H$ and $V$ be bounded self-adjoint operators. If $V$ is compact then $E_{H+V}(J)-E_{H}(J)$ is a compact operator.

(Solved) Example: $u$ not a weak limit point but $Ku$ a strong limit point, where $K$ a compact operator on Hilbert space.

If $T_{1}$ is dominated by $T_{2}$ and $T_{2}$ is a compact operator, can we deduce that $T_{1}$ is a compact operator?

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