List questions from spectral-theory

Published on 02 Nov 2016 - 16:45

237

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Banach Subalgebras: Spectrum

Published on 27 Mar 2026 - 22:30

680

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Resolvent set of Volterra integral operator

Published on 25 Mar 2026 - 4:39

2.4k

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Why is the spectrum of an operator with compact resolvent countable and consists only of eigenvalues?

Published on 27 Mar 2026 - 16:25

1.3k

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Shape of spectrum of bounded linear operator on complex Banach space

Published on 10 Nov 2016 - 23:52

39

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$T\in\mathcal{B}(X)$ with $T^{2}=0\implies\sigma(T)=\{0\}$

Published on 12 Nov 2016 - 20:35

120

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Spectrum: Products

Published on 12 Nov 2016 - 20:39

1.8k

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A spectrum of an invertible operator does not contain $0$

Published on 26 Mar 2026 - 3:11

1.5k

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Self-adjoint Operator Properties

Published on 13 Nov 2016 - 4:52

266

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Partial ordering of the positivity in a C-star algebra

Published on 13 Nov 2016 - 12:47

44

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If $В$ is an arbitrary member of the inner product space, show that $L_b$ is unitarily equivalent to $R_{B^t}$.

Published on 13 Nov 2016 - 14:12

116

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Why is the point spectrum of the operator $(Tx)(t)=\int_{0}^{t}x(s)ds$, for $x\in C[0,1]$, empty?

Published on 13 Nov 2016 - 16:16

185

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Cauchy-Schwarz and spectral gap

Published on 14 Nov 2016 - 2:57

146

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hear a 3D drum as a solid shape or as a surface

Published on 14 Nov 2016 - 9:36

114

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Why do the eigenfunctions of a 1D Schroedinger operator with even potential alternate in parity?

Published on 14 Nov 2016 - 17:03

List Question

Does boundedness of $\sigma(T)$ imply boundedness of $T$, $T$ an operator on a Banach space?

Banach Subalgebras: Spectrum

Resolvent set of Volterra integral operator

Why is the spectrum of an operator with compact resolvent countable and consists only of eigenvalues?

Shape of spectrum of bounded linear operator on complex Banach space

$T\in\mathcal{B}(X)$ with $T^{2}=0\implies\sigma(T)=\{0\}$

Spectrum: Products

A spectrum of an invertible operator does not contain $0$

Self-adjoint Operator Properties

Partial ordering of the positivity in a C-star algebra

If $В$ is an arbitrary member of the inner product space, show that $L_b$ is unitarily equivalent to $R_{B^t}$.

Why is the point spectrum of the operator $(Tx)(t)=\int_{0}^{t}x(s)ds$, for $x\in C[0,1]$, empty?

Cauchy-Schwarz and spectral gap

hear a 3D drum as a solid shape or as a surface

Why do the eigenfunctions of a 1D Schroedinger operator with even potential alternate in parity?

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