List questions from spectral-theory

Published on 11 Aug 2014 - 17:46

129

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Spectra of operators on different spaces

Published on 11 Aug 2014 - 19:06

294

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Skew-adjoint differential operator $B$ with spectrum $\sigma(B)=i(-\infty,-1]$

Published on 12 Aug 2014 - 15:10

106

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Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Published on 13 Aug 2014 - 7:09

129

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Prove that spec$(f(A)) = f$(spec$(A)).$

Published on 14 Aug 2014 - 2:26

144

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Non-Unitarily Diagonalizable Matrices

Published on 14 Aug 2014 - 5:37

50

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Normal Matrices Unitarily Diagonazible

Published on 14 Aug 2014 - 7:11

81

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Spectral decomposition of a Hilbert space

Published on 14 Aug 2014 - 9:11

620

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Prove that for a bounded self adjoint operator, $\langle Tx,x\rangle \geq 0$ is equivalent to $\sigma(T)\subset [0,\infty)$

Published on 16 Aug 2014 - 0:37

50

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Just a translation issue.

Published on 17 Aug 2014 - 8:57

132

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Spectrum of $Tu=\int^1_{-1} (1-|x-y|)u(y)dy $

Published on 25 Mar 2026 - 23:52

118

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Finding the smallest max eigenvalues for related matrices?

Published on 25 Mar 2026 - 14:21

139

Views

Resolvent and spectrum of a self-adjoint extension

Published on 19 Aug 2014 - 7:02

1.3k

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Continuity of the spectral radius

Published on 25 Mar 2026 - 22:02

737

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Why is the Gelfand transform injective?

Published on 26 Mar 2026 - 19:32

List Question

Resolvent set of extension

Spectra of operators on different spaces

Skew-adjoint differential operator $B$ with spectrum $\sigma(B)=i(-\infty,-1]$

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Prove that spec$(f(A)) = f$(spec$(A)).$

Non-Unitarily Diagonalizable Matrices

Normal Matrices Unitarily Diagonazible

Spectral decomposition of a Hilbert space

Prove that for a bounded self adjoint operator, $\langle Tx,x\rangle \geq 0$ is equivalent to $\sigma(T)\subset [0,\infty)$

Just a translation issue.

Spectrum of $Tu=\int^1_{-1} (1-|x-y|)u(y)dy $

Finding the smallest max eigenvalues for related matrices?

Resolvent and spectrum of a self-adjoint extension

Continuity of the spectral radius

Why is the Gelfand transform injective?

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