List questions from operator-theory

Published on 24 Mar 2026 - 23:46

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Is the following claim true?

Published on 22 Mar 2026 - 2:50

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

Published on 25 Mar 2026 - 10:48

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Bounded projection

Published on 20 Mar 2026 - 2:34

158

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$AB$ is compact iff $BA$ is

Published on 21 Mar 2026 - 14:41

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

Published on 24 Mar 2026 - 23:44

332

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Eigenvalues of certain Hankel matrix

Published on 25 Mar 2026 - 9:48

31

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Necessary condition for Hermician lin operators

Published on 24 Mar 2026 - 4:18

40

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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 22 Mar 2026 - 9:45

397

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Injectivity and the lower bound of an operator

Published on 22 Mar 2026 - 15:18

55

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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 20 Mar 2026 - 9:53

80

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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 22 Mar 2026 - 8:30

293

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Sufficient conditions for contraction mapping for unbounded functions?

Published on 24 Jan 2018 - 12:38

186

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Some properties of linear and compact operators

Published on 22 Mar 2026 - 15:13

81

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Operator in a generic Hilbert space $H$

Published on 25 Mar 2026 - 2:59

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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