List questions from compact-operators

Published on 26 Mar 2026 - 18:59

281

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Let $(a_n)\subset\mathbb{C}$ be bounded. Then $T_a\colon\ell^p\to\ell^p, \ (T_a x)_n:=a_n x_n$ compact iff $a_n\to0$.

Published on 26 Mar 2026 - 19:02

51

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$f_x:c_0\to c_0$ given by $ (y_i)_{i\in \mathbb{N}} \mapsto ((x_i^2)y_i)_{i\in \mathbb{N}}$ is compact.

Published on 26 Mar 2026 - 19:01

115

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Spectrum of compact operator on an infinite dimensional Banach space

Published on 26 Mar 2026 - 19:00

70

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Classification of compact multiplication operators

Published on 26 Mar 2026 - 18:59

124

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Examples of continuous nonlinear operators in PDE

Published on 26 Mar 2026 - 19:05

179

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Existence of Polynomial P such that P(A)=0

Published on 26 Mar 2026 - 19:00

92

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$T_{a}(\text{ball}(\ell^p))$ is compact, where $T_a\colon\ell^p\to\ell^p$, $(T_a x)_{n}:=a_{n}x_{n}$ and $\mathbb{C}\ni a_n\to0$ as $n\to\infty$

Published on 26 Mar 2026 - 19:02

144

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The compactness of an operator from $C[0,1]$ to $C[0,1]$

Published on 26 Mar 2026 - 19:00

78

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Example of an integral operator satisfying Holmgren's condition but not compact

Published on 26 Mar 2026 - 19:00

175

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Is this a compact operator?

Published on 26 Mar 2026 - 19:04

112

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Prove that $\ker(\lambda Id-T)$ stabilizes for some $n\in \Bbb N$

Published on 26 Mar 2026 - 19:05

1.1k

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What does algebraic multiplicity mean for compact operators

Published on 26 Mar 2026 - 18:59

116

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The definition of compact operator

Published on 26 Mar 2026 - 19:05

102

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Why is $S\colon\ell^{2}\to\ell^{2}$ defined by $(Sx)_{m}:=\sum_{n\in\mathbb{N}}a_{m,n}x_{n}$ a compact operator?

Published on 26 Mar 2026 - 19:03

List Question

Weak-strong continuous non-compact operator $c_0 \to \ell_1$

Let $(a_n)\subset\mathbb{C}$ be bounded. Then $T_a\colon\ell^p\to\ell^p, \ (T_a x)_n:=a_n x_n$ compact iff $a_n\to0$.

$f_x:c_0\to c_0$ given by $ (y_i)_{i\in \mathbb{N}} \mapsto ((x_i^2)y_i)_{i\in \mathbb{N}}$ is compact.

Spectrum of compact operator on an infinite dimensional Banach space

Classification of compact multiplication operators

Examples of continuous nonlinear operators in PDE

Existence of Polynomial P such that P(A)=0

$T_{a}(\text{ball}(\ell^p))$ is compact, where $T_a\colon\ell^p\to\ell^p$, $(T_a x)_{n}:=a_{n}x_{n}$ and $\mathbb{C}\ni a_n\to0$ as $n\to\infty$

The compactness of an operator from $C[0,1]$ to $C[0,1]$

Example of an integral operator satisfying Holmgren's condition but not compact

Is this a compact operator?

Prove that $\ker(\lambda Id-T)$ stabilizes for some $n\in \Bbb N$

What does algebraic multiplicity mean for compact operators

The definition of compact operator

Why is $S\colon\ell^{2}\to\ell^{2}$ defined by $(Sx)_{m}:=\sum_{n\in\mathbb{N}}a_{m,n}x_{n}$ a compact operator?

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