List questions from hilbert-spaces

Published on 04 Jun 2018 - 20:02

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Proof that every bounded linear operator between hilbert spaces has an adjoint.

Published on 26 Mar 2026 - 1:01

46

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Is $\big\{x \in L^2[0,1]:\int_0^1x(t)\,dt=0\big\}$ a closed set?

Published on 06 Jun 2018 - 4:54

216

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Polynomial and operator in Hilbert space

Published on 25 Mar 2026 - 9:31

26

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A question about the assumptions of Galerkin's Method

Published on 25 Mar 2026 - 6:10

204

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How to calculate the integral ${\langle\psi|\overrightarrow{r}|\psi\rangle}=\frac{\alpha^3}{\pi}\int_{V}\overrightarrow{r} e^{-2\alpha r}dV$

Published on 26 Mar 2026 - 16:07

161

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Counterexample(?) of the theorem An Orthonormal basis of a vector space X is a Hamel basis if and only if X is finite dimensional.

Published on 25 Mar 2026 - 0:04

105

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Find a Unique Bounded Linear Mapping in the Hilbert Space

Published on 25 Mar 2026 - 6:19

259

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Quasinilpotent operators satisfying a polynomial identity

Published on 26 Mar 2026 - 12:53

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$A:H \to H$, $Ax = \sum_{n=1}^{\infty} s_{n} \langle x, e_{n} \rangle f_{n}$, $s_{n} \searrow 0$, $e_{n}$, $f_{n}$ orthonormal bases of H

Published on 25 Mar 2026 - 11:21

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Which of these subsets are dense in $l^2$?

Published on 25 Mar 2026 - 21:48

147

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$L^2$ norm on a product space $]0,1[\times \Omega$

Published on 11 Jun 2018 - 0:40

68

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Orthogonal complement in Hilbert space

Published on 11 Jun 2018 - 10:45

61

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How to show that the following set is compact.

Published on 25 Mar 2026 - 21:49

93

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Given any sequence $(\alpha_n) \in l^2$, the series $\sum_{k=1}^{\infty} \alpha_k e_k$ converges to some element $u \in H$

Published on 11 Jun 2018 - 23:55

List Question

Projection on Hilbert spaces

Proof that every bounded linear operator between hilbert spaces has an adjoint.

Is $\big\{x \in L^2[0,1]:\int_0^1x(t)\,dt=0\big\}$ a closed set?

Polynomial and operator in Hilbert space

A question about the assumptions of Galerkin's Method

How to calculate the integral ${\langle\psi|\overrightarrow{r}|\psi\rangle}=\frac{\alpha^3}{\pi}\int_{V}\overrightarrow{r} e^{-2\alpha r}dV$

Counterexample(?) of the theorem An Orthonormal basis of a vector space X is a Hamel basis if and only if X is finite dimensional.

Find a Unique Bounded Linear Mapping in the Hilbert Space

Quasinilpotent operators satisfying a polynomial identity

$A:H \to H$, $Ax = \sum_{n=1}^{\infty} s_{n} \langle x, e_{n} \rangle f_{n}$, $s_{n} \searrow 0$, $e_{n}$, $f_{n}$ orthonormal bases of H

Which of these subsets are dense in $l^2$?

$L^2$ norm on a product space $]0,1[\times \Omega$

Orthogonal complement in Hilbert space

How to show that the following set is compact.

Given any sequence $(\alpha_n) \in l^2$, the series $\sum_{k=1}^{\infty} \alpha_k e_k$ converges to some element $u \in H$

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