List questions from compact-operators

Published on 10 Apr 2026 - 5:41

80

Views

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 15 Apr 2026 - 15:40

32

Views

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 15 Apr 2026 - 12:12

72

Views

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 12 Apr 2026 - 9:21

390

Views

Operator norm of integral operator

Published on 11 May 2026 - 13:11

172

Views

Schauder fixed point extended

Published on 11 May 2026 - 2:08

117

Views

Is weakly continuous operator weakly compact?

Published on 09 Apr 2026 - 20:04

256

Views

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

Published on 16 Apr 2026 - 8:31

220

Views

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

Published on 10 Apr 2026 - 21:07

405

Views

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

Published on 10 May 2026 - 15:10

56

Views

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

Published on 16 Apr 2026 - 19:40

70

Views

Reference request on operators with compact powers

Published on 17 Apr 2026 - 5:31

72

Views

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

Published on 09 Apr 2026 - 19:33

369

Views

Prove that the following map is compact

Published on 14 Apr 2026 - 21:55

64

Views

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

Published on 15 Apr 2026 - 0:27

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 $\dim \ker (\text{id}-A) < + \infty$.

Trending Questions

Popular # Hahtags

Popular Questions