List questions from spectral-theory

Published on 25 Mar 2026 - 20:39

61

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Spectra of $\{A_k\}_{k=1}^\infty \cup \{A_\infty\}$ and Continuity of the Spectrum

Published on 31 May 2023 - 7:46

99

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If $A$ is a densely defined linear operator with a compact inverse, is the spectrum of $A$ dicrete?

Published on 28 Mar 2026 - 4:35

82

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Difference between $L^2[0,2\pi]$ and $L^2(S^1)$

Published on 06 Jun 2023 - 17:43

89

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Proving that restriction of linear operator to invariant set has same eigenvectors as linear operator

Published on 30 Mar 2026 - 10:11

140

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Intuitively, why does the spectral gap control the speed of convergence to equilibrium.

Published on 26 Mar 2026 - 13:01

66

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Operator whose spectrum is different from the spectrum of its dual

Published on 08 Jun 2023 - 19:27

54

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Numerical range of unbounded symmetric but not selfadjoint operator!

Published on 10 Jun 2023 - 14:01

25

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Stability theorem for (matrix-valued) eigenvalues of compact self-adjoint operators

Published on 28 Mar 2026 - 4:33

47

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Spectral Mapping Theorem. Does $\|(A-\lambda)x_k\| \to 0$ imply $\| (g(A)-g(\lambda))x_k\| \to 0$?

Published on 14 Jun 2023 - 14:58

38

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Eigenvectors of Normal Operators

Published on 28 Mar 2026 - 4:33

53

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Equivalent criterion for invertiblity of a normal operator in an Hilbert space.

Published on 25 Mar 2026 - 19:05

94

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The norm, resolvent set, and adjoint of the operator $T(x_1, x_2, \ldots) = (x_2, x_3, \ldots)$ on $\ell_1$

Published on 22 Jun 2023 - 4:37

106

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Strong limit of $A^n$ and $A^{1/n}$ for a positive operator

Published on 26 Mar 2026 - 6:31

27

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Does Dissipative system have point Koopman spectrum or continuous Koopman spectrum?

Published on 23 Feb 2026 - 10:16

List Question

An exercise about normal operators

Spectra of $\{A_k\}_{k=1}^\infty \cup \{A_\infty\}$ and Continuity of the Spectrum

If $A$ is a densely defined linear operator with a compact inverse, is the spectrum of $A$ dicrete?

Difference between $L^2[0,2\pi]$ and $L^2(S^1)$

Proving that restriction of linear operator to invariant set has same eigenvectors as linear operator

Intuitively, why does the spectral gap control the speed of convergence to equilibrium.

Operator whose spectrum is different from the spectrum of its dual

Numerical range of unbounded symmetric but not selfadjoint operator!

Stability theorem for (matrix-valued) eigenvalues of compact self-adjoint operators

Spectral Mapping Theorem. Does $\|(A-\lambda)x_k\| \to 0$ imply $\| (g(A)-g(\lambda))x_k\| \to 0$?

Eigenvectors of Normal Operators

Equivalent criterion for invertiblity of a normal operator in an Hilbert space.

The norm, resolvent set, and adjoint of the operator $T(x_1, x_2, \ldots) = (x_2, x_3, \ldots)$ on $\ell_1$

Strong limit of $A^n$ and $A^{1/n}$ for a positive operator

Does Dissipative system have point Koopman spectrum or continuous Koopman spectrum?

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