List questions from hilbert-spaces

Published on 28 Mar 2026 - 22:55

31

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Is the function mapping a self-adjoint operator on a Hilbert space to the maximum of its spectrum differentiable?

Published on 28 Mar 2026 - 20:59

415

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Orthonormal basis for Hilbert Schmidt operators

Published on 11 Oct 2019 - 2:25

140

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homomorphisms of B(H)

Published on 30 Mar 2026 - 3:19

34

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Representation formula for the $n$th power of a self-adjoint operator in terms of the spectral measure

Published on 29 Mar 2026 - 0:00

145

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Is the image by a closed range operator of a closed subspace closed too?

Published on 11 Oct 2019 - 15:55

127

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Boundedness of the Hilbert-Hankel operator on $L^p(\mathbb{R^+})$

Published on 31 Mar 2026 - 20:59

66

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Bilinear map $m:B(H)\times H\to H$

Published on 25 Mar 2026 - 23:38

189

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Examples of Vector space whose Basis $\not\subset$ Vector space

Published on 13 Oct 2019 - 7:37

36

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$F = \{f \in C^{1}([a,b]): f(a) = 0\}$ not complete

Published on 13 Oct 2019 - 23:54

447

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A bounded, self-adjoint, positive operator $T$ induces a positive semidefinite quadratic form $\langle Tx,x\rangle$.

Published on 29 Mar 2026 - 3:36

175

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rigorous use of parseval identity for derivative to prove an inequality

Published on 23 Feb 2026 - 1:22

302

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Exterior algebra for infinite dimensional vector spaces

Published on 26 Mar 2026 - 8:12

182

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show that $\sum_{n=1}^{\infty}\alpha_n x_n$ converges in $H$ if and only if $\sum_{n=1}^{\infty}|\alpha_n|^2<\infty$.

Published on 14 Oct 2019 - 16:22

36

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if $F:X\to X$ is continuous, such that for some $\mu>0$, $\left \langle F(u), u \right \rangle\geq 0$ for all $u\in X$ with $||u||=\mu$

Published on 27 Mar 2026 - 22:53

List Question

Dense subset of Hilbert space

Is the function mapping a self-adjoint operator on a Hilbert space to the maximum of its spectrum differentiable?

Orthonormal basis for Hilbert Schmidt operators

homomorphisms of B(H)

Representation formula for the $n$th power of a self-adjoint operator in terms of the spectral measure

Is the image by a closed range operator of a closed subspace closed too?

Boundedness of the Hilbert-Hankel operator on $L^p(\mathbb{R^+})$

Bilinear map $m:B(H)\times H\to H$

Examples of Vector space whose Basis $\not\subset$ Vector space

$F = \{f \in C^{1}([a,b]): f(a) = 0\}$ not complete

A bounded, self-adjoint, positive operator $T$ induces a positive semidefinite quadratic form $\langle Tx,x\rangle$.

rigorous use of parseval identity for derivative to prove an inequality

Exterior algebra for infinite dimensional vector spaces

show that $\sum_{n=1}^{\infty}\alpha_n x_n$ converges in $H$ if and only if $\sum_{n=1}^{\infty}|\alpha_n|^2<\infty$.

if $F:X\to X$ is continuous, such that for some $\mu>0$, $\left \langle F(u), u \right \rangle\geq 0$ for all $u\in X$ with $||u||=\mu$

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