List questions from compact-operators

Published on 03 May 2026 - 8:55

421

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Bijective compact operator between $X$ and $Y$ with $\text{dim}(X)=\infty$?

Published on 05 May 2026 - 10:01

153

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Numerical radius of the absolute value of an operator

Published on 15 Apr 2026 - 7:24

842

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Convolution operator

Published on 03 May 2026 - 0:14

1.6k

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Showing that the Hilbert-Schmidt integral operator is compact.

Published on 12 Apr 2026 - 5:02

99

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If $A,B$ are self-adjoint and $A+B\ge 0$, then $A_+-B_-,\ B_+-A_-\ge 0$?

Published on 10 May 2026 - 13:50

187

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The Image of the Closed Unit Ball Under Finite Rank Operators

Published on 15 Apr 2026 - 10:22

288

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A equality in the proof of $T$ compact $\iff T^*$ compact

Published on 12 Apr 2026 - 6:41

252

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Cesàro summation in Hilbert space

Published on 12 Apr 2026 - 21:28

314

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Limit of sequence of finite rank operators given by $(A_Nf)(x) = \sum_{n=-N}^N \hat f(n) e^{inx}$ is the identity operator, so how can it be compact?

Published on 15 Apr 2026 - 14:25

265

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Prove convergence in operator norm and compact operator

Published on 20 Apr 2026 - 8:08

2.1k

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Compact operator can be approximated by finite rank operator

Published on 13 Apr 2026 - 14:57

45

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$E$ Banach space, $K: E \to E$ compact $\Rightarrow$ if $\lambda \neq 0 \in \sigma(K)$, $\lambda$ is eigenvalue

Published on 14 Apr 2026 - 6:18

700

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Uniform Convergence of Sequence of Bounded Operators

Published on 14 Apr 2026 - 14:39

59

Views

Square Root of Operator forms a two sided ideal

Published on 12 Apr 2026 - 1:19

List Question

Importance of compact operators for numerical approximation of integral equations?

Bijective compact operator between $X$ and $Y$ with $\text{dim}(X)=\infty$?

Numerical radius of the absolute value of an operator

Convolution operator

Showing that the Hilbert-Schmidt integral operator is compact.

If $A,B$ are self-adjoint and $A+B\ge 0$, then $A_+-B_-,\ B_+-A_-\ge 0$?

The Image of the Closed Unit Ball Under Finite Rank Operators

A equality in the proof of $T$ compact $\iff T^*$ compact

Cesàro summation in Hilbert space

Limit of sequence of finite rank operators given by $(A_Nf)(x) = \sum_{n=-N}^N \hat f(n) e^{inx}$ is the identity operator, so how can it be compact?

Prove convergence in operator norm and compact operator

Compact operator can be approximated by finite rank operator

$E$ Banach space, $K: E \to E$ compact $\Rightarrow$ if $\lambda \neq 0 \in \sigma(K)$, $\lambda$ is eigenvalue

Uniform Convergence of Sequence of Bounded Operators

Square Root of Operator forms a two sided ideal

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