List questions from spectral-theory

Published on 25 Mar 2026 - 14:00

39

Views

Does a spectral theorem exist for linear operator pencils?

Published on 07 Apr 2026 - 16:38

106

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Why does the determinant of the Dirac operator on $S^n$ approach $1$ as $n\to\infty$?

Published on 25 Mar 2026 - 22:26

79

Views

Rayleigh quotient of a vector permutation

Published on 26 Mar 2026 - 14:19

77

Views

Determining what happens to the spectrum of Schrödinger operator as boundary condition changes

Published on 16 Sep 2020 - 19:00

139

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Positivity of a Sturm-Liouville operator

Published on 29 Mar 2026 - 19:11

48

Views

For self-adjoint $A$ and $B$, when is $(A+iB)^*$ the closure of $A-iB$?

Published on 17 Sep 2020 - 12:40

86

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For a bounded linear operator $T$ and $\alpha\in\mathbb{C}$, show the spectrum $\sigma(\alpha T)=\alpha\sigma(T)$

Published on 18 Sep 2020 - 8:14

478

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If $A^k$ is the identity matrix for some $k \geq 2$, then $A^2$ is the identity matrix

Published on 19 Sep 2020 - 0:08

312

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Prove that the resolvent set of an operator is an open set

Published on 20 Sep 2020 - 7:09

254

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Can the Laplacian of two graphs have the same eigenvectors but different eigenvalues?

Published on 26 Mar 2026 - 4:30

113

Views

Holomorphic functional calculus

Published on 01 Oct 2020 - 11:05

67

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T bounded is compact if and only if $\sigma_{\mathrm{ess}}(T)=\{0\}$.

Published on 26 Mar 2026 - 14:24

66

Views

Question regarding the application of Cauchy's integral formula in the proof of Gelfands spectral radius formula.

Published on 02 Oct 2020 - 16:18

238

Views

Proof that the continuous part of a spectrum really is "interval like"?

Published on 26 Mar 2026 - 14:25

List Question

Mercer theorem and uniformly bounded continuous function

Does a spectral theorem exist for linear operator pencils?

Why does the determinant of the Dirac operator on $S^n$ approach $1$ as $n\to\infty$?

Rayleigh quotient of a vector permutation

Determining what happens to the spectrum of Schrödinger operator as boundary condition changes

Positivity of a Sturm-Liouville operator

For self-adjoint $A$ and $B$, when is $(A+iB)^*$ the closure of $A-iB$?

For a bounded linear operator $T$ and $\alpha\in\mathbb{C}$, show the spectrum $\sigma(\alpha T)=\alpha\sigma(T)$

If $A^k$ is the identity matrix for some $k \geq 2$, then $A^2$ is the identity matrix

Prove that the resolvent set of an operator is an open set

Can the Laplacian of two graphs have the same eigenvectors but different eigenvalues?

Holomorphic functional calculus

T bounded is compact if and only if $\sigma_{\mathrm{ess}}(T)=\{0\}$.

Question regarding the application of Cauchy's integral formula in the proof of Gelfands spectral radius formula.

Proof that the continuous part of a spectrum really is "interval like"?

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