List questions from hilbert-spaces

124

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$\| (I-T)^{-1}|_{\ker(I-T)^\perp} \| \geq 1$ for all compact operator $T$ in an infinite dimensional Hilbert space

Published on 18 Mar 2026 - 18:44

121

Views

hyponormal operators

Published on 21 Mar 2026 - 19:21

130

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a positive matrix of operators

Published on 22 Mar 2026 - 1:15

54

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If $S=(S_1,S_2)$ hyponormal, why $S_1$ and $S_2$ are hyponormal?

Published on 24 Mar 2026 - 2:12

3.9k

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Is the cartesian product of two Hilbert spaces a Hilbert space?

Published on 23 Mar 2026 - 19:18

184

Views

Show that $ Tf $ is continuous and measurable on a Hilbert space $H=L_2((0,\infty))$

Published on 20 Mar 2026 - 3:15

114

Views

Kernel functions for vectors in discrete spaces

Published on 22 Mar 2026 - 12:23

93

Views

The space $D(A^\infty)$

Published on 21 Mar 2026 - 21:47

82

Views

Show that $Tf$ is well-defined and is continious

Published on 24 Mar 2026 - 8:25

73

Views

construction of a sequence in a complex Hilbert space which fulfills some specific properties

Published on 23 Mar 2026 - 6:38

206

Views

If $A\in\mathcal{L}(E)$, why $\lim\limits_{n\to+\infty}\|A^n\|^{1/n}$ always exists?

Published on 19 Mar 2026 - 23:13

285

Views

Sobolev space $H^s(Q)$ is Hilbert

Published on 20 Mar 2026 - 2:36

82

Views

Unbounded self-adjoint "nth-root"operators

Published on 20 Mar 2026 - 2:07

49

Views

Compactness of the resolvent - references

Published on 23 Mar 2026 - 14:31

44

Views

Equivalent property of a positiv definite operator

Published on 22 Mar 2026 - 18:47

List Question

$\| (I-T)^{-1}|_{\ker(I-T)^\perp} \| \geq 1$ for all compact operator $T$ in an infinite dimensional Hilbert space

hyponormal operators

a positive matrix of operators

If $S=(S_1,S_2)$ hyponormal, why $S_1$ and $S_2$ are hyponormal?

Is the cartesian product of two Hilbert spaces a Hilbert space?

Show that $ Tf $ is continuous and measurable on a Hilbert space $H=L_2((0,\infty))$

Kernel functions for vectors in discrete spaces

The space $D(A^\infty)$

Show that $Tf$ is well-defined and is continious

construction of a sequence in a complex Hilbert space which fulfills some specific properties

If $A\in\mathcal{L}(E)$, why $\lim\limits_{n\to+\infty}\|A^n\|^{1/n}$ always exists?

Sobolev space $H^s(Q)$ is Hilbert

Unbounded self-adjoint "nth-root"operators

Compactness of the resolvent - references

Equivalent property of a positiv definite operator

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