List questions from hilbert-spaces

Published on 25 Mar 2026 - 6:32

60

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Proving a space is not complete by finding an absolutely convergent series

Published on 22 Mar 2026 - 21:14

44

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If in a orthogonal basis of a Hilbert space H, i take off just one element, do i get a strict subpsace of H?

Published on 25 Feb 2018 - 15:01

121

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Orthogonality of eigenvectors of a positive operator in the polar decomposition

Published on 25 Mar 2026 - 9:40

459

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Example of infinite dimensional linear spaces where the space is equal to its dual.

Published on 24 Mar 2026 - 22:13

89

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Verifying two (simple) inequalities about projections

Published on 28 Feb 2018 - 13:03

557

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Is Schatten p-norm a monotone ideal norm?

Published on 28 Feb 2018 - 16:38

461

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if $T\in B(H)$ has closed range then show that $T ^*$ also have closed range.

Published on 01 Mar 2018 - 13:03

66

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IF $||T||\leq 1$ Then, $T(I-T^{}T)^{1/2}$ = $(I-TT^{})^{1/2}T$

Published on 01 Mar 2018 - 13:22

52

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Show a bounded operator is scalar multiple of identity operator

Published on 01 Mar 2018 - 15:18

195

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Show that no two eigenvectors of adjoint of right shift operator are orthogonal

Published on 01 Mar 2018 - 18:23

105

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A problem on compact operator

Published on 01 Mar 2018 - 19:57

225

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Why is this unbounded operator self-adjoint?

Published on 01 Mar 2018 - 20:17

68

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If $Q$ is a nonnegative operator on a Hilbert space $U$, show that $\langle Q^{1/2}u_0,Q^{1/2}v_0\rangle_{Q^{1/2}U}=\langle u_0,v_0\rangle_{Q^{1/2}U}$

Published on 22 Mar 2026 - 13:57

184

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Proof explanation about tensor product of operators

Published on 04 Mar 2018 - 10:33

List Question

Reference Request: Infinite-Dimensional Analysis

Proving a space is not complete by finding an absolutely convergent series

If in a orthogonal basis of a Hilbert space H, i take off just one element, do i get a strict subpsace of H?

Orthogonality of eigenvectors of a positive operator in the polar decomposition

Example of infinite dimensional linear spaces where the space is equal to its dual.

Verifying two (simple) inequalities about projections

Is Schatten p-norm a monotone ideal norm?

if $T\in B(H)$ has closed range then show that $T ^*$ also have closed range.

IF $||T||\leq 1$ Then, $T(I-T^{}T)^{1/2}$ = $(I-TT^{})^{1/2}T$

Show a bounded operator is scalar multiple of identity operator

Show that no two eigenvectors of adjoint of right shift operator are orthogonal

A problem on compact operator

Why is this unbounded operator self-adjoint?

If $Q$ is a nonnegative operator on a Hilbert space $U$, show that $\langle Q^{1/2}u_0,Q^{1/2}v_0\rangle_{Q^{1/2}U}=\langle u_0,v_0\rangle_{Q^{1/2}U}$

Proof explanation about tensor product of operators

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