List questions from hilbert-spaces

Published on 26 Mar 2026 - 13:30

55

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Convergence to the differential operator

Published on 25 Mar 2026 - 3:18

146

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A question about a generalization of covariance

Published on 25 Mar 2026 - 20:10

62

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Infinite tensor product identity

Published on 10 Feb 2019 - 15:14

81

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Common eigenfunctions of 0 eigenvalue for the angular momentum components

Published on 27 Mar 2026 - 9:37

105

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Proving $|\int_{0}^{x}{f(t)\,dt|^2} \le 2x^{1/2}\int_{0}^{x}{t^{1/2}| f(t)|^2\,dt}$ for $f \in L^2[0,\infty)$ and $x \geq 0$

Published on 29 Mar 2026 - 5:44

74

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Orthonormal $\{e_n\}$ is complete in $L^2[a,b]$ iff $\sum_{n=1}^{\infty} \mid \int_{a}^{x} e_n(t) dt \mid^2 = x-a$ for all $x \in [a,b]$.

Published on 26 Mar 2026 - 1:11

151

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If $(H_λ)_{λ≥0}$ is a spectral decomposition and $π_λ$ is the orthogonal projection onto $H_λ$, then $t↦π_λ$ is increasing and right-continuous

Published on 25 Mar 2026 - 19:32

117

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an equivalent condition for $B(H,K)$ to be a Hilbert space

Published on 12 Feb 2019 - 5:04

70

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Integrability with respect to a spectral measure

Published on 25 Mar 2026 - 21:01

164

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Approximating orthonormal basis in Hilbert space by orthonormal basis from dense subset

Published on 26 Mar 2026 - 1:10

67

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Show {$e^{2\pi i bnx}$} is a basis for $L^2[0,b^{-1}]$

Published on 12 Feb 2019 - 23:33

49

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Why can an element of a Hilbert space be written as this sum?

Published on 27 Mar 2026 - 10:46

712

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Proving Compactness in $\ell^2$ by total boundedness

Published on 13 Feb 2019 - 15:34

1000

Views

Probability on Hilbert spaces

Published on 13 Feb 2019 - 15:43

List Question

Dual of compact operator and dimension of dual space

Convergence to the differential operator

A question about a generalization of covariance

Infinite tensor product identity

Common eigenfunctions of 0 eigenvalue for the angular momentum components

Proving $|\int_{0}^{x}{f(t)\,dt|^2} \le 2x^{1/2}\int_{0}^{x}{t^{1/2}| f(t)|^2\,dt}$ for $f \in L^2[0,\infty)$ and $x \geq 0$

Orthonormal $\{e_n\}$ is complete in $L^2[a,b]$ iff $\sum_{n=1}^{\infty} \mid \int_{a}^{x} e_n(t) dt \mid^2 = x-a$ for all $x \in [a,b]$.

If $(H_λ)_{λ≥0}$ is a spectral decomposition and $π_λ$ is the orthogonal projection onto $H_λ$, then $t↦π_λ$ is increasing and right-continuous

an equivalent condition for $B(H,K)$ to be a Hilbert space

Integrability with respect to a spectral measure

Approximating orthonormal basis in Hilbert space by orthonormal basis from dense subset

Show {$e^{2\pi i bnx}$} is a basis for $L^2[0,b^{-1}]$

Why can an element of a Hilbert space be written as this sum?

Proving Compactness in $\ell^2$ by total boundedness

Probability on Hilbert spaces

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