Question

Does this sequence of unit vectors in a Hilbert space converge?

score 53 · Answer 1 · 2026-03-25 18:47:15

53

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Does this sequence of unit vectors in a Hilbert space converge?

Published on 25 Mar 2026 - 18:47

score 48 · Answer 2 · 2026-03-26 06:33:36

48

Views

Brezis' exercise 5.25.3

Published on 26 Mar 2026 - 6:33

score 37 · Answer 3 · 2026-03-26 04:53:49

37

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Restriction of self-adjoint operator to the vectors orthogonal to a finite-dimensional subspace

Published on 26 Mar 2026 - 4:53

score 50 · Answer 4 · 2026-04-12 00:00:26

50

Views

If $A,B\in\mathcal{B}(\mathcal{H}):AB=BA$ and $A$ does not have an inverse, then $AB$ does not have an inverse

Published on 12 Apr 2026 - 0:00

score 188 · Answer 5 · 2026-04-09 03:53:10

188

Views

Composition of nonexpansive and averaged operators

Published on 09 Apr 2026 - 3:53

score 119 · Answer 6 · 2026-04-13 19:15:45

119

Views

Is it true that $\langle \left(P(\mathbb{1}_A)\right)^2, \mathbb{1}_A\ \rangle \geq \mu(A)^2$?

Published on 13 Apr 2026 - 19:15

score 58 · Answer 7 · 2026-04-05 18:11:41

58

Views

Brezis' exercise 5.27

Published on 05 Apr 2026 - 18:11

score 135 · Answer 8 · 2026-04-14 06:56:43

135

Views

$H$ is Hilbert Space, select $x_n\in H$ such that $||x_n||=n$ then $\exists x \in H$ such that $\sup_n |(x_n,x)|=\infty$

Published on 14 Apr 2026 - 6:56

score 49 · Answer 9 · 2026-03-28 07:38:32

49

Views

$\lim_{n}||T_n||\not\to 0\implies\sum_{n=0}^\infty T_n$ cannot converge in operator norm topology for self-adjoint $T_n\in\mathcal{B}(\mathcal{H})$

Published on 28 Mar 2026 - 7:38

score 75 · Answer 10 · 2026-04-08 16:38:10

75

Views

Green function of a Schrodinger operator

Published on 08 Apr 2026 - 16:38

score 66 · Answer 11 · 2026-04-13 01:00:20

66

Views

Showing that if $V$ is a closed invariant subspace under $A\in B(H)$ then $V$ is invariant under $f(A)$ for any bounded measurable $f$

Published on 13 Apr 2026 - 1:00

score 69 · Answer 12 · 2026-04-06 06:18:19

69

Views

Brezis' exercise 5.25.6: weak convergence of Cesàro mean

Published on 06 Apr 2026 - 6:18

score 228 · Answer 13 · 2026-04-13 03:00:58

228

Views

span of maximal orthonormal sets in a Hilbert space

Published on 13 Apr 2026 - 3:00

score 34 · Answer 14 · 2023-05-15 12:38:46

34

Views

Why does $\sum_{n=0}^\infty P_n\psi$ converge in norm for $\{P_n\}_n$ a sequence of orthogonal projections on a Hilbert space $H$?

Published on 15 May 2023 - 12:38

score 40 · Answer 15 · 2026-04-10 16:54:58

40

Views

What does it mean to integrate some complex valued function with respect to a projection valued measure of an operator in functional calculus?

Published on 10 Apr 2026 - 16:54

List Question

Does this sequence of unit vectors in a Hilbert space converge?

Brezis' exercise 5.25.3

Restriction of self-adjoint operator to the vectors orthogonal to a finite-dimensional subspace

If $A,B\in\mathcal{B}(\mathcal{H}):AB=BA$ and $A$ does not have an inverse, then $AB$ does not have an inverse

Composition of nonexpansive and averaged operators

Is it true that $\langle \left(P(\mathbb{1}_A)\right)^2, \mathbb{1}_A\ \rangle \geq \mu(A)^2$?

Brezis' exercise 5.27

$H$ is Hilbert Space, select $x_n\in H$ such that $||x_n||=n$ then $\exists x \in H$ such that $\sup_n |(x_n,x)|=\infty$

$\lim_{n}||T_n||\not\to 0\implies\sum_{n=0}^\infty T_n$ cannot converge in operator norm topology for self-adjoint $T_n\in\mathcal{B}(\mathcal{H})$

Green function of a Schrodinger operator

Showing that if $V$ is a closed invariant subspace under $A\in B(H)$ then $V$ is invariant under $f(A)$ for any bounded measurable $f$

Brezis' exercise 5.25.6: weak convergence of Cesàro mean

span of maximal orthonormal sets in a Hilbert space

Why does $\sum_{n=0}^\infty P_n\psi$ converge in norm for $\{P_n\}_n$ a sequence of orthogonal projections on a Hilbert space $H$?

What does it mean to integrate some complex valued function with respect to a projection valued measure of an operator in functional calculus?

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