List questions from operator-theory

Published on 13 Apr 2026 - 13:18

109

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If $L$ is a continuous linear form on a dense subspace of a Hilbert space $H$, what do we mean by the claim $L\in H$?

Published on 14 Apr 2026 - 23:08

170

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Not every positive operator is positive-definite operator

Published on 08 Apr 2026 - 20:50

1k

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Resolvent of a Self-Adjoint Operator

Published on 09 Apr 2026 - 12:25

4.8k

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Norm of the Resolvent

Published on 11 Apr 2026 - 16:43

836

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Definition of the Laplacian as an operator from $H_0^1(\Omega)$ to $H_0^1(\Omega)'$

Published on 13 Apr 2026 - 18:46

2k

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Spectrum of the Resolvent of a Self-Adjoint Operator

Published on 10 Apr 2026 - 3:57

297

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Universal $C^*$ algebras

Published on 16 Apr 2026 - 13:17

77

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Showing space is complete and functional is bounded

Published on 11 Apr 2026 - 16:28

47

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Fibers of unbounded linear functional are dense

Published on 13 Apr 2026 - 19:54

44

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Exercise on the operator $g(t)\mapsto \sqrt \lambda g(\lambda t)$

Published on 16 Apr 2026 - 2:04

43

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For which $\alpha$ is this integral operator compact?

Published on 12 Apr 2026 - 3:33

761

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Trace norm of a triangular matrix with only ones above the diagonal

Published on 13 Apr 2026 - 8:02

86

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Determining whether equality $ \|T v\| = \|T\| \cdot \|v\|$ is possible

Published on 12 Apr 2026 - 15:44

408

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Proving an operator is compact exercise

Published on 09 Apr 2026 - 21:41

List Question

Integral operator convergence study in $L^2(\mathbb{R})$

If $L$ is a continuous linear form on a dense subspace of a Hilbert space $H$, what do we mean by the claim $L\in H$?

Not every positive operator is positive-definite operator

Resolvent of a Self-Adjoint Operator

Norm of the Resolvent

Definition of the Laplacian as an operator from $H_0^1(\Omega)$ to $H_0^1(\Omega)'$

Spectrum of the Resolvent of a Self-Adjoint Operator

Universal $C^*$ algebras

Showing space is complete and functional is bounded

Fibers of unbounded linear functional are dense

Exercise on the operator $g(t)\mapsto \sqrt \lambda g(\lambda t)$

For which $\alpha$ is this integral operator compact?

Trace norm of a triangular matrix with only ones above the diagonal

Determining whether equality $ \|T v\| = \|T\| \cdot \|v\|$ is possible

Proving an operator is compact exercise

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