List questions from unbounded-operators

Published on 09 Apr 2026 - 16:46

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What is the relation between linear, continuous, bounded and compact operators?

Published on 12 Apr 2026 - 22:43

72

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$C^1$-Functions as the domain closure of differentiation the polynomials

Published on 16 Apr 2026 - 10:01

66

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Is the functional mapping $x$ to the statistical limit of $x$ bounded (continuous)?

Published on 11 Apr 2026 - 5:23

1.8k

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Definition of a closable operator

Published on 09 Apr 2026 - 13:25

305

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The limit functional on the sequence space of all convergent sequences is bounded functional with norm 1

Published on 14 Apr 2026 - 6:27

42

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Unbounded operator and generator

Published on 09 Apr 2026 - 4:56

739

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Closed operator with trivial resolvent set

Published on 10 Apr 2026 - 14:51

410

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Definition of a reducing subspace

Published on 12 Apr 2026 - 17:16

176

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Functional calculus for unbounded positve operator

Published on 09 Apr 2026 - 21:29

458

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Spectral theorem for harmonic oscillator

Published on 14 Apr 2026 - 0:11

676

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Show $\{f \in L^2[0,1] : f \text{ is absolutely continuous},\ f\ '\in L^2[0,1],\ f(0)=f(1)=0\}$ is dense in $L^2[0,1]$.

Published on 16 Apr 2026 - 22:52

81

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Spectral measure of an eigenvector

Published on 10 May 2026 - 19:46

857

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If $T$ is self-adjoint then $T^2$ is also self-adjoint,

Published on 10 May 2026 - 19:48

75

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Is it a mistake if I delete the condition in Banach - Steinhaus Theorem?

Published on 10 May 2026 - 20:39

List Question

Spectra of Closure and Adjoint for Symmetric Operator

What is the relation between linear, continuous, bounded and compact operators?

$C^1$-Functions as the domain closure of differentiation the polynomials

Is the functional mapping $x$ to the statistical limit of $x$ bounded (continuous)?

Definition of a closable operator

The limit functional on the sequence space of all convergent sequences is bounded functional with norm 1

Unbounded operator and generator

Closed operator with trivial resolvent set

Definition of a reducing subspace

Functional calculus for unbounded positve operator

Spectral theorem for harmonic oscillator

Show $\{f \in L^2[0,1] : f \text{ is absolutely continuous},\ f\ '\in L^2[0,1],\ f(0)=f(1)=0\}$ is dense in $L^2[0,1]$.

Spectral measure of an eigenvector

If $T$ is self-adjoint then $T^2$ is also self-adjoint,

Is it a mistake if I delete the condition in Banach - Steinhaus Theorem?

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