List questions from compact-operators

Published on 25 Mar 2026 - 8:12

75

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Open Maps in $\mathcal{B}(X, Y)$ form an open set

Published on 29 Apr 2023 - 3:04

228

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On the Fredholm Alternative for PDE's in Evan's book

Published on 27 Mar 2026 - 10:10

62

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$K(H)$ is maximal if $H$ is separable.

Published on 07 May 2023 - 17:20

64

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Show that resolvent of $L:=-\partial_v (\partial_v +v)$ is compact

Published on 09 May 2023 - 14:26

61

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Showing $l^p\to l^p,(x_n)_n\mapsto(a_nx_n)_n$ is compact iff $a_n\to0$

Published on 17 May 2023 - 10:14

32

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Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Published on 19 May 2023 - 14:42

64

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Showing an operator is not compact

Published on 21 May 2023 - 8:44

54

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About the injectivity and surjectivity of the map $T = (\lambda I - K)|_{\mathfrak{R}}$

Published on 22 May 2023 - 10:36

40

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For which values of the parameter $r$ the operator is compact?

Published on 25 May 2023 - 17:44

55

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Showing non-compactness of an operator on $L^2(-1,1)$ by finding a bounded sequence with no convergent subsequence

Published on 28 May 2023 - 19:23

41

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Show that there exists $0 \neq v_0 \in H$ with $v_0 \perp V$ such that the supremum is attained.

Published on 29 May 2023 - 15:33

68

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Confusion regarding the proof of $\mathscr{I}_1(H)$ (trace class operators on $H$) is Banach space with respect to $\lVert\cdot\rVert_1$.

Published on 29 May 2023 - 15:47

69

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$T(\varphi_k) = \frac{1}{k}\varphi_{k+1}$ is compact but has no eigenvector

Published on 30 May 2023 - 1:28

123

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Asymptotics of orthonormal basis in $\ell^2$

Published on 01 Jun 2023 - 4:31

List Question

Representation of semigroup of trace-class operators in terms of projectors

Open Maps in $\mathcal{B}(X, Y)$ form an open set

On the Fredholm Alternative for PDE's in Evan's book

$K(H)$ is maximal if $H$ is separable.

Show that resolvent of $L:=-\partial_v (\partial_v +v)$ is compact

Showing $l^p\to l^p,(x_n)_n\mapsto(a_nx_n)_n$ is compact iff $a_n\to0$

Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Showing an operator is not compact

About the injectivity and surjectivity of the map $T = (\lambda I - K)|_{\mathfrak{R}}$

For which values of the parameter $r$ the operator is compact?

Showing non-compactness of an operator on $L^2(-1,1)$ by finding a bounded sequence with no convergent subsequence

Show that there exists $0 \neq v_0 \in H$ with $v_0 \perp V$ such that the supremum is attained.

Confusion regarding the proof of $\mathscr{I}_1(H)$ (trace class operators on $H$) is Banach space with respect to $\lVert\cdot\rVert_1$.

$T(\varphi_k) = \frac{1}{k}\varphi_{k+1}$ is compact but has no eigenvector

Asymptotics of orthonormal basis in $\ell^2$

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