List questions from compact-operators

Published on 21 Feb 2019 - 3:35

77

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If $\|A(x)\|_Y \geq c \|x\|_X$ and $\dim X = + \infty$, can $A \in \mathcal{L}(X,Y)$ be a compact operator?

Published on 23 Feb 2019 - 10:49

29

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Showing that $0 \in \overline{A(\partial B_1^X)}$ if $X,Y$ Banach with $\dim X = + \infty$ and $A \in \mathcal{L}_c(X,Y)$.

Published on 23 Feb 2019 - 19:32

69

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Showing that $\exists x \in H : \|A(x)\| = \|A\|_\mathcal{L}$ if $H$ is Hilbert and $A \in \mathcal{L}_c(X,Y)$.

Published on 24 Feb 2019 - 10:44

382

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Operator norm of integral operator

Published on 23 Mar 2026 - 7:42

168

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Schauder fixed point extended

Published on 26 Feb 2019 - 19:37

114

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Is weakly continuous operator weakly compact?

Published on 01 Mar 2019 - 15:17

253

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If $X$ is reflexive and $A \in \mathcal{L}(c_0,X)$ then show that $A$ is a compact operator.

Published on 02 Mar 2019 - 21:36

217

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Norm of AB+BA when A, B are well understood

Published on 04 Mar 2019 - 0:55

402

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$C^*$ algebra of compact operators as a direct limit of matrix algebras?

Published on 25 Mar 2026 - 1:18

51

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$A(D) \subseteq Y$ is compact if $A \in \mathcal{L}_c(X,Y)$, $X$ reflexive, $Y$ Banach and $D$ closed, convex and bounded.

Published on 05 Mar 2019 - 16:07

65

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Reference request on operators with compact powers

Published on 05 Mar 2019 - 18:25

69

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How is $\Bbb K$ well defined, operator algebra

Published on 06 Mar 2019 - 16:01

366

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Prove that the following map is compact

Published on 06 Mar 2019 - 23:28

61

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If $A \in \mathcal{L}_c(X)$ and $X$ is Banach, then $\dim \ker (\text{id}-A) < + \infty$.

Published on 13 Mar 2019 - 16:15

List Question

Compact operators and Fredholm's theory

If $\|A(x)\|_Y \geq c \|x\|_X$ and $\dim X = + \infty$, can $A \in \mathcal{L}(X,Y)$ be a compact operator?

Showing that $0 \in \overline{A(\partial B_1^X)}$ if $X,Y$ Banach with $\dim X = + \infty$ and $A \in \mathcal{L}_c(X,Y)$.

Showing that $\exists x \in H : \|A(x)\| = \|A\|_\mathcal{L}$ if $H$ is Hilbert and $A \in \mathcal{L}_c(X,Y)$.

Operator norm of integral operator

Schauder fixed point extended

Is weakly continuous operator weakly compact?

If $X$ is reflexive and $A \in \mathcal{L}(c_0,X)$ then show that $A$ is a compact operator.

Norm of AB+BA when A, B are well understood

$C^*$ algebra of compact operators as a direct limit of matrix algebras?

$A(D) \subseteq Y$ is compact if $A \in \mathcal{L}_c(X,Y)$, $X$ reflexive, $Y$ Banach and $D$ closed, convex and bounded.

Reference request on operators with compact powers

How is $\Bbb K$ well defined, operator algebra

Prove that the following map is compact

If $A \in \mathcal{L}_c(X)$ and $X$ is Banach, then $\dim \ker (\text{id}-A) < + \infty$.

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