Question

If $M$ is the span of a finite orthonormal set in a Hilbert space then $M$ is closed

score 697 · Answer 1 · 2026-05-01 11:41:47

697

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If $M$ is the span of a finite orthonormal set in a Hilbert space then $M$ is closed

Published on 01 May 2026 - 11:41

score 513 · Answer 2 · 2026-04-11 21:12:50

513

Views

Orthogonal sum with non-closed subspace

Published on 11 Apr 2026 - 21:12

score 46 · Answer 3 · 2026-04-16 07:34:07

46

Views

Prove that $d(T_1,T_2)=\|T_1-T_2\|$ is a metric on $V$

Published on 16 Apr 2026 - 7:34

score 33 · Answer 4 · 2026-04-10 16:13:27

33

Views

question related to the norm of bounded linear operator

Published on 10 Apr 2026 - 16:13

score 124 · Answer 5 · 2026-04-11 04:45:54

124

Views

Clarifications on the Gelfand triple $V \subset H \subset V^*$

Published on 11 Apr 2026 - 4:45

score 3.6k · Answer 6 · 2026-05-10 15:02:08

3.6k

Views

Spectrum of unitary operators lie in the unit circle

Published on 10 May 2026 - 15:02

score 821 · Answer 7 · 2026-05-07 14:30:09

821

Views

Hilbert space basis which is not a vector space basis

Published on 07 May 2026 - 14:30

score 408 · Answer 8 · 2026-04-13 22:42:09

408

Views

When can an infinite matrix have uniformly bounded rows and columns in $\ell^2$ but not be bounded on $\ell^2$.

Published on 13 Apr 2026 - 22:42

score 313 · Answer 9 · 2026-05-10 14:55:43

313

Views

linear operator on inner product space with $(B,A)=\operatorname{tr}(AB^\dagger)$

Published on 10 May 2026 - 14:55

score 824 · Answer 10 · 2026-04-13 22:57:46

824

Views

Number of nonzero Fourier coefficients for any $x$ can be at most countably many

Published on 13 Apr 2026 - 22:57

score 111 · Answer 11 · 2026-04-17 07:25:09

111

Views

Is $S_M(0,1)$ always homeomorphic to the unit sphere of $E$?

Published on 17 Apr 2026 - 7:25

score 91 · Answer 12 · 2026-04-21 11:59:45

91

Views

Can I write $\mathcal H: \{c_n\} \to \{(n+\frac{1}{2})c_n\}$ as $H=\operatorname{diag}(\frac{1}{2}, 1 +\frac{1}{2}, 2+\frac{1}{2}, ...) $?

Published on 21 Apr 2026 - 11:59

score 64 · Answer 13 · 2026-04-17 14:06:43

64

Views

why $\|Sx\|=\sup_{\|y\| \le 1} |\langle Sx, y \rangle|,\;\forall x\in E?$

Published on 17 Apr 2026 - 14:06

score 384 · Answer 14 · 2026-04-15 10:02:54

384

Views

If $A$ is a self-adjoint operator . Is $\|A^n\|=\|A\|^n,\;\forall n$?

Published on 15 Apr 2026 - 10:02

score 166 · Answer 15 · 2026-04-15 13:17:05

166

Views

Show that a set is complete in an Hilbert space $H$

Published on 15 Apr 2026 - 13:17

List Question

If $M$ is the span of a finite orthonormal set in a Hilbert space then $M$ is closed

Orthogonal sum with non-closed subspace

Prove that $d(T_1,T_2)=\|T_1-T_2\|$ is a metric on $V$

question related to the norm of bounded linear operator

Clarifications on the Gelfand triple $V \subset H \subset V^*$

Spectrum of unitary operators lie in the unit circle

Hilbert space basis which is not a vector space basis

When can an infinite matrix have uniformly bounded rows and columns in $\ell^2$ but not be bounded on $\ell^2$.

linear operator on inner product space with $(B,A)=\operatorname{tr}(AB^\dagger)$

Number of nonzero Fourier coefficients for any $x$ can be at most countably many

Is $S_M(0,1)$ always homeomorphic to the unit sphere of $E$?

Can I write $\mathcal H: \{c_n\} \to \{(n+\frac{1}{2})c_n\}$ as $H=\operatorname{diag}(\frac{1}{2}, 1 +\frac{1}{2}, 2+\frac{1}{2}, ...) $?

why $\|Sx\|=\sup_{\|y\| \le 1} |\langle Sx, y \rangle|,\;\forall x\in E?$

If $A$ is a self-adjoint operator . Is $\|A^n\|=\|A\|^n,\;\forall n$?

Show that a set is complete in an Hilbert space $H$

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