List questions from compact-operators

159

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How does the definition of compactness imply that all continuous operators are compact in finite dimensional spaces?

Published on 13 Sep 2015 - 17:12

181

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Looking for a general approach to proving compactness of linear operators.

Published on 23 Sep 2015 - 13:05

1.4k

Views

Compactness of the trace operator

Published on 23 Sep 2015 - 17:02

100

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$\mathcal{A}+K$ is norm-closed where $\mathcal{A}$ is a $C^*$-algebra and $K$ is the compact operators.

Published on 29 Sep 2015 - 3:42

87

Views

C*-algebraic intrinsic definition for compactness of an operator?

Published on 06 Oct 2015 - 18:22

78

Views

Prove compactness of an operator.

Published on 08 Oct 2015 - 5:25

667

Views

$T$ is a compact operator but not a finite rank operator

Published on 10 Mar 2026 - 6:09

38

Views

Functional Analysis, infimum of $A+K$ where $K\in K(X)$

Published on 26 Oct 2015 - 17:19

560

Views

Are Hilbert-Schmidt operators in non-separable Hilbert spaces compact?

Published on 02 Nov 2015 - 1:15

115

Views

Strong convergence due to Compact Operator

Published on 24 Mar 2026 - 2:56

3.8k

Views

T compact if and only if $T^*T$ is compact.

Published on 29 Nov 2015 - 8:04

67

Views

Prove the following are equivalent.

Published on 24 Mar 2026 - 22:01

322

Views

Compactness of a certain Integral Operator on $L^2$

Published on 29 Nov 2015 - 10:47

91

Views

Measure of non-compactness

Published on 01 Dec 2015 - 9:45

234

Views

Eigenvalues of an integral operator

Published on 25 Mar 2026 - 23:13

List Question

How does the definition of compactness imply that all continuous operators are compact in finite dimensional spaces?

Looking for a general approach to proving compactness of linear operators.

Compactness of the trace operator

$\mathcal{A}+K$ is norm-closed where $\mathcal{A}$ is a $C^*$-algebra and $K$ is the compact operators.

C*-algebraic intrinsic definition for compactness of an operator?

Prove compactness of an operator.

$T$ is a compact operator but not a finite rank operator

Functional Analysis, infimum of $A+K$ where $K\in K(X)$

Are Hilbert-Schmidt operators in non-separable Hilbert spaces compact?

Strong convergence due to Compact Operator

T compact if and only if $T^*T$ is compact.

Prove the following are equivalent.

Compactness of a certain Integral Operator on $L^2$

Measure of non-compactness

Eigenvalues of an integral operator

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