Question

If $(\lambda_i)$ are the eigenvalues of $A$, then $\sum_{i=1}^k\lambda_i=\sup_{\text{rank}B=k}\langle AB,B\rangle_{HS}$

score 132 · Answer 1 · 2026-03-28 22:08:17

132

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If $(\lambda_i)$ are the eigenvalues of $A$, then $\sum_{i=1}^k\lambda_i=\sup_{\text{rank}B=k}\langle AB,B\rangle_{HS}$

Published on 28 Mar 2026 - 22:08

score 57 · Answer 2 · 2026-02-23 10:14:13

57

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General question about functional calculus

Published on 23 Feb 2026 - 10:14

score 103 · Answer 3 · 2026-03-27 01:47:41

103

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examples of a compact operator $K: l^2 \to l^2$ with point spectrum $\sigma_p(K)=\{0,1,\frac{1}{2},\frac{1}{3},...\}$, with finite and infinite kernel

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score 327 · Answer 4 · 2026-03-27 03:41:08

327

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isolated point of spectrum of compact self-adjoint linear operator on infinite-dimensional separable Hilbert space.

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score 241 · Answer 5 · 2020-04-08 23:41:29

241

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Proof of the spectral theorem for compact operators in Banach spaces

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score 223 · Answer 6 · 2026-03-26 13:01:09

223

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$\rho(B) \leq \rho(|B|)$, where $\rho$ is the spectral radius

Published on 26 Mar 2026 - 13:01

score 45 · Answer 7 · 2020-04-11 04:38:51

45

Views

How to solve this eigenvalue problem?

Published on 11 Apr 2020 - 4:38

score 228 · Answer 8 · 2026-03-26 11:00:48

228

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spectral radius formula - why does $\sum \xi^n \zeta^{-n}$ converge for $|\zeta| > r(\xi)$?

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score 98 · Answer 9 · 2020-04-12 08:58:14

98

Views

Show that the spectrum of $S$ is a countable set.

Published on 12 Apr 2020 - 8:58

score 654 · Answer 10 · 2020-04-13 05:06:20

654

Views

Example of a Bounded Linear Operator with Unbounded Spectrum.

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score 329 · Answer 11 · 2020-04-13 18:51:50

329

Views

Spectrum of an operator on $\ell^1$

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score 99 · Answer 12 · 2026-03-27 16:53:58

99

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Relation of spectral multiplicity and commutant

Published on 27 Mar 2026 - 16:53

score 115 · Answer 13 · 2026-03-25 17:43:46

115

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score 277 · Answer 14 · 2026-03-29 06:30:17

277

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Possible significant error in proof of the spectral theorem, Brian C Hall, Quantum Theory for Mathematicians

Published on 29 Mar 2026 - 6:30

score 174 · Answer 15 · 2020-04-16 23:43:56

174

Views

Show that eigen-vectors belong in range of projection valued measure.

Published on 16 Apr 2020 - 23:43

List Question

If $(\lambda_i)$ are the eigenvalues of $A$, then $\sum_{i=1}^k\lambda_i=\sup_{\text{rank}B=k}\langle AB,B\rangle_{HS}$

General question about functional calculus

examples of a compact operator $K: l^2 \to l^2$ with point spectrum $\sigma_p(K)=\{0,1,\frac{1}{2},\frac{1}{3},...\}$, with finite and infinite kernel

isolated point of spectrum of compact self-adjoint linear operator on infinite-dimensional separable Hilbert space.

Proof of the spectral theorem for compact operators in Banach spaces

$\rho(B) \leq \rho(|B|)$, where $\rho$ is the spectral radius

How to solve this eigenvalue problem?

spectral radius formula - why does $\sum \xi^n \zeta^{-n}$ converge for $|\zeta| > r(\xi)$?

Show that the spectrum of $S$ is a countable set.

Example of a Bounded Linear Operator with Unbounded Spectrum.

Spectrum of an operator on $\ell^1$

Relation of spectral multiplicity and commutant

Different proof of spectral theorem for self-adjoint operators

Possible significant error in proof of the spectral theorem, Brian C Hall, Quantum Theory for Mathematicians

Show that eigen-vectors belong in range of projection valued measure.

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