List questions from spectral-theory

Published on 02 Apr 2026 - 23:17

18

Views

If $\lambda,\mu\in\rho(T)$ and $(T-\lambda)D_0$ is dense in $X$ then $(T-\mu)D_0$ is dense in $X$.

Published on 18 Mar 2026 - 10:30

171

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Borel operator calculus of compound function

Published on 30 Oct 2020 - 9:10

87

Views

The set $\mathbb{C} \setminus \sigma(x)$ is connected.

Published on 01 Apr 2026 - 0:55

37

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Proving a spectrum is a subset of another

Published on 31 Oct 2020 - 10:48

131

Views

Spectrum of operator $T: \ell^{2}\supset\text{dom}(T) \rightarrow \ell^{2}$ defined by $(x_{n})_{n\in \mathbb{N}} \mapsto (nx_{n})_{n\in \mathbb {N}}$

Published on 02 Nov 2020 - 14:25

865

Views

Spectrum of adjoint of linear operator

Published on 03 Nov 2020 - 11:25

89

Views

Stability of PDE and the relation with Discrete spectrum/continuous spectrum

Published on 25 Mar 2026 - 7:48

352

Views

Jacobi operator's spectrum in $l_2$

Published on 04 Nov 2020 - 18:11

165

Views

counterexample of $\rho(AB) \leq \rho(A)\rho(B)$

Published on 26 Mar 2026 - 22:54

184

Views

Show that $\rho(A) \geq \max_{1\leq i \leq n}|a_{ii}|.$

Published on 26 Mar 2026 - 22:58

193

Views

Spectrum of integral operator $A$: $(A f)t = \int_0^t f$ by definition of $Sp$

Published on 09 Nov 2020 - 15:32

136

Views

Spectral theorem, inner products and adjoints/transposes: what's the relation?

Published on 10 Nov 2020 - 17:30

433

Views

Spectrum of direct sum and direct integral included in the union of the spectra of its constituents

Published on 31 Mar 2026 - 5:26

109

Views

Continuous versus Discrete Spectrum in Ergodic Theory

Published on 07 Apr 2026 - 22:10

List Question

Spectrum (eigenvalues) and their relation to Projection Valued Measures(PVM)

If $\lambda,\mu\in\rho(T)$ and $(T-\lambda)D_0$ is dense in $X$ then $(T-\mu)D_0$ is dense in $X$.

Borel operator calculus of compound function

The set $\mathbb{C} \setminus \sigma(x)$ is connected.

Proving a spectrum is a subset of another

Spectrum of operator $T: \ell^{2}\supset\text{dom}(T) \rightarrow \ell^{2}$ defined by $(x_{n})_{n\in \mathbb{N}} \mapsto (nx_{n})_{n\in \mathbb {N}}$

Spectrum of adjoint of linear operator

Stability of PDE and the relation with Discrete spectrum/continuous spectrum

Jacobi operator's spectrum in $l_2$

counterexample of $\rho(AB) \leq \rho(A)\rho(B)$

Show that $\rho(A) \geq \max_{1\leq i \leq n}|a_{ii}|.$

Spectrum of integral operator $A$: $(A f)t = \int_0^t f$ by definition of $Sp$

Spectral theorem, inner products and adjoints/transposes: what's the relation?

Spectrum of direct sum and direct integral included in the union of the spectra of its constituents

Continuous versus Discrete Spectrum in Ergodic Theory

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