List questions from hilbert-spaces

Published on 22 Jul 2016 - 1:01

341

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Space of $f(0)=f(1)$: Is Hilbert space?

Published on 04 Apr 2026 - 7:26

113

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Compact operator problem: $I-T$ is onto, then $I-T$ is invertible?

Published on 23 Jul 2016 - 21:59

54

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If $(V,\left<.,.\right>)$ is hilbert, show that $\sum_{k=1}^\infty \left<v,e_i\right>e_i=v$

Published on 24 Jul 2016 - 17:49

67

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Lower bound on gap between consecutive eigenvalues on $L_2(\mathbb{R}^3)$

Published on 30 Mar 2026 - 14:37

41

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Existence of Fourier Series

Published on 05 Apr 2026 - 23:19

101

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$ι:U→V$ is an embedding, $Q:=ιι^$, $L∈(ℝ^d)$, $Φ∈\text{HS}(U,ℝ^d)$ $⇒$ $\text{tr}LΦ\sqrt Q(Φ\sqrt Q)^$ doesn't depend on $ι$

Published on 29 Mar 2026 - 7:29

153

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Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space

Published on 05 Apr 2026 - 16:24

148

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Trace norm of a superposition of rank one operators

Published on 29 Jul 2016 - 10:12

33

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Basis whose integral is a basis

Published on 27 Mar 2026 - 23:30

254

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Adjoint Operator and Subspaces of Hilbert Spaces

Published on 27 Mar 2026 - 19:32

73

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Similarity and restriction of an operator

Published on 04 Aug 2016 - 4:12

215

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Does parallel make sense in arbitrary vector spaces?

Published on 08 Apr 2026 - 3:36

575

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Dealing with Linear Spans in an Infinite-Dimensional Space

Published on 25 Mar 2026 - 7:41

504

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Unitary transformations relating two arbitrary normed vectors in an infinite dimensional Hilbert space?

Published on 06 Aug 2016 - 5:15

List Question

Basis of convex and concave functions

Space of $f(0)=f(1)$: Is Hilbert space?

Compact operator problem: $I-T$ is onto, then $I-T$ is invertible?

If $(V,\left<.,.\right>)$ is hilbert, show that $\sum_{k=1}^\infty \left<v,e_i\right>e_i=v$

Lower bound on gap between consecutive eigenvalues on $L_2(\mathbb{R}^3)$

Existence of Fourier Series

$ι:U→V$ is an embedding, $Q:=ιι^$, $L∈(ℝ^d)$, $Φ∈\text{HS}(U,ℝ^d)$ $⇒$ $\text{tr}LΦ\sqrt Q(Φ\sqrt Q)^$ doesn't depend on $ι$

Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space

Trace norm of a superposition of rank one operators

Basis whose integral is a basis

Adjoint Operator and Subspaces of Hilbert Spaces

Similarity and restriction of an operator

Does parallel make sense in arbitrary vector spaces?

Dealing with Linear Spans in an Infinite-Dimensional Space

Unitary transformations relating two arbitrary normed vectors in an infinite dimensional Hilbert space?

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