List questions from operator-theory

Published on 04 May 2026 - 8:42

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Is the following claim true?

Published on 11 Apr 2026 - 0:26

170

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Proving that a composition of bounded operator and trace class operator is trace class

Published on 17 Apr 2026 - 23:49

2.7k

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Bounded projection

Published on 30 Apr 2026 - 2:15

167

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$AB$ is compact iff $BA$ is

Published on 29 Apr 2026 - 12:26

366

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Why $\sup_{\substack{x\in E,\\ \|x\|=1}}\|Ax\|\geq\sup_{\substack{x\in E,\\ \|x\|\leq1}}\|Ax\|?$

Published on 10 May 2026 - 12:32

335

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Eigenvalues of certain Hankel matrix

Published on 29 Apr 2026 - 12:55

40

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Necessary condition for Hermician lin operators

Published on 29 Apr 2026 - 12:08

46

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Is $\lim_{n\to \infty} L {\varphi_n} = L \lim_{n\to \infty} {\varphi_n}$ for $L=I-A$ where $A$ is compact?

Published on 05 May 2026 - 4:12

400

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Injectivity and the lower bound of an operator

Published on 11 Apr 2026 - 11:55

67

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Show directly that if $E_1\geqslant E_2\geqslant\dots$, then $E_i\rightarrow \bigwedge E_i$ strongly.

Published on 02 May 2026 - 20:18

86

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Is it possible to construct a compact operator $A$ such that all polynomials of degree $1$ are in the nullspace of $I-A$?

Published on 05 May 2026 - 4:14

296

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Sufficient conditions for contraction mapping for unbounded functions?

Published on 09 Apr 2026 - 16:48

196

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Some properties of linear and compact operators

Published on 10 May 2026 - 12:49

83

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Operator in a generic Hilbert space $H$

Published on 11 Apr 2026 - 2:16

List Question

Explain a proof about the norm of derivation of operators

Is the following claim true?

Proving that a composition of bounded operator and trace class operator is trace class

Bounded projection

$AB$ is compact iff $BA$ is

Why $\sup_{\substack{x\in E,\\ \|x\|=1}}\|Ax\|\geq\sup_{\substack{x\in E,\\ \|x\|\leq1}}\|Ax\|?$

Eigenvalues of certain Hankel matrix

Necessary condition for Hermician lin operators

Is $\lim_{n\to \infty} L {\varphi_n} = L \lim_{n\to \infty} {\varphi_n}$ for $L=I-A$ where $A$ is compact?

Injectivity and the lower bound of an operator

Show directly that if $E_1\geqslant E_2\geqslant\dots$, then $E_i\rightarrow \bigwedge E_i$ strongly.

Is it possible to construct a compact operator $A$ such that all polynomials of degree $1$ are in the nullspace of $I-A$?

Sufficient conditions for contraction mapping for unbounded functions?

Some properties of linear and compact operators

Operator in a generic Hilbert space $H$

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