List questions from spectral-theory

Published on 07 May 2026 - 12:41

167

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Power spectrum of field over an arbitrarily-shaped country

Published on 07 May 2026 - 7:42

245

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Calculating spectrum and resolvent set of a linear operator (General question).

Published on 02 May 2026 - 18:18

655

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Operator with compact resolvent

Published on 29 Apr 2026 - 12:26

132

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bounded below operator/ Kato-Rellich

Published on 29 Apr 2026 - 12:26

67

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Show directly that if $E_1\geqslant E_2\geqslant\dots$, then $E_i\rightarrow \bigwedge E_i$ strongly.

Published on 02 May 2026 - 20:18

693

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Is the spectral radius less than $1$?

Published on 07 May 2026 - 12:19

237

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How to show range of a projection is an eigenspace.

Published on 02 May 2026 - 18:20

102

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Spectral radius inequality for non-abelian Banach algebras

Published on 07 May 2026 - 16:52

1.9k

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Do unitarily equivalent operators have the same spectrum?

Published on 07 May 2026 - 7:35

136

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Spectral theorem for inductive limits of $C^*$-Algebras

Published on 29 Apr 2026 - 13:37

157

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Showing that $\inf_{\|x\|=1}\langle Tx,x\rangle$ and $\sup_{\|x\|=1}\langle Tx,x\rangle$ are eigenvalues of $T$ (in particular when they are $0$)

Published on 29 Apr 2026 - 12:08

207

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Characterization of the resolvent of a bounded operator on a Hilbert space

Published on 10 May 2026 - 12:34

115

Views

Confusion in definition of peripheral spectrum

Published on 23 Apr 2026 - 0:37

93

Views

Simple exercise on spectral measures

Published on 10 May 2026 - 13:46

List Question

Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?

Power spectrum of field over an arbitrarily-shaped country

Calculating spectrum and resolvent set of a linear operator (General question).

Operator with compact resolvent

bounded below operator/ Kato-Rellich

Show directly that if $E_1\geqslant E_2\geqslant\dots$, then $E_i\rightarrow \bigwedge E_i$ strongly.

Is the spectral radius less than $1$?

How to show range of a projection is an eigenspace.

Spectral radius inequality for non-abelian Banach algebras

Do unitarily equivalent operators have the same spectrum?

Spectral theorem for inductive limits of $C^*$-Algebras

Showing that $\inf_{\|x\|=1}\langle Tx,x\rangle$ and $\sup_{\|x\|=1}\langle Tx,x\rangle$ are eigenvalues of $T$ (in particular when they are $0$)

Characterization of the resolvent of a bounded operator on a Hilbert space

Confusion in definition of peripheral spectrum

Simple exercise on spectral measures

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