List questions from hilbert-spaces

Published on 28 Mar 2026 - 22:55

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Problem of dual space from krieszig functional analysis

Published on 20 Oct 2019 - 7:43

21

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$z\in M^\perp$ iff $\|z\|=d(z,M)$?

Published on 20 Oct 2019 - 11:12

267

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Is the continous spectrum of a self-adjoint operator always uncountable?

Published on 29 Mar 2026 - 1:35

72

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$H^m(\Omega)=\{u\in D'(\Omega): \partial^{\alpha}u\in L^2(\Omega) \forall \alpha, |\alpha|\leq m \}$ is a Hilbert space

Published on 28 Mar 2026 - 1:07

67

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Extend $T$ to a bounded linear operator...

Published on 21 Oct 2019 - 18:58

58

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A closed set in Hilbert space does not have infimum norm

Published on 22 Oct 2019 - 2:01

218

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Compact Operators limit of Projections (finite rank)

Published on 26 Mar 2026 - 17:35

28

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Let $(V,\left \langle .,. \right \rangle)$ be a space of Hilbert and $F\in V'$. Then $U=\{v\in V: F(v)=0\}$ is a closed subspace of $V$.

Published on 02 Apr 2026 - 2:12

48

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compactness of the operator $Tx (t) = t x(t)$ ($0< t < 1 $)

Published on 26 Mar 2026 - 17:35

42

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Show that $P_Eh=h- \langle h,e_1 \rangle_1 - \langle h,e_2 \rangle e_2$ for $E=\{e_1,e_2\}^\perp$

Published on 23 Oct 2019 - 6:53

1.1k

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Multiplication Operator on $L^2( \mathbb{R})$ is not Compact

Published on 26 Mar 2026 - 17:35

16

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Generalization of the matrix in $l^2_{\mathbb{C}}(\mathbb{Z})$

Published on 24 Oct 2019 - 18:40

43

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Implications of relative operator bounds.

Published on 28 Mar 2026 - 22:31

93

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$\ker(A)^\perp=\operatorname{Im}(A)$

Published on 25 Oct 2019 - 17:18

List Question

Determine if $g=\sum_{n=1}^\infty n^{-1/3}e_n$ exists in Hilbert space

Problem of dual space from krieszig functional analysis

$z\in M^\perp$ iff $\|z\|=d(z,M)$?

Is the continous spectrum of a self-adjoint operator always uncountable?

$H^m(\Omega)=\{u\in D'(\Omega): \partial^{\alpha}u\in L^2(\Omega) \forall \alpha, |\alpha|\leq m \}$ is a Hilbert space

Extend $T$ to a bounded linear operator...

A closed set in Hilbert space does not have infimum norm

Compact Operators limit of Projections (finite rank)

Let $(V,\left \langle .,. \right \rangle)$ be a space of Hilbert and $F\in V'$. Then $U=\{v\in V: F(v)=0\}$ is a closed subspace of $V$.

compactness of the operator $Tx (t) = t x(t)$ ($0< t < 1 $)

Show that $P_Eh=h- \langle h,e_1 \rangle_1 - \langle h,e_2 \rangle e_2$ for $E=\{e_1,e_2\}^\perp$

Multiplication Operator on $L^2( \mathbb{R})$ is not Compact

Generalization of the matrix in $l^2_{\mathbb{C}}(\mathbb{Z})$

Implications of relative operator bounds.

$\ker(A)^\perp=\operatorname{Im}(A)$

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