Question

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

score 688 · Answer 1 · 2026-03-23 06:23:09

688

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

Published on 23 Mar 2026 - 6:23

score 510 · Answer 2 · 2018-02-12 03:42:24

510

Views

Orthogonal sum with non-closed subspace

Published on 12 Feb 2018 - 3:42

score 43 · Answer 3 · 2018-02-12 04:35:10

43

Views

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

Published on 12 Feb 2018 - 4:35

score 30 · Answer 4 · 2018-02-12 18:03:35

30

Views

question related to the norm of bounded linear operator

Published on 12 Feb 2018 - 18:03

score 121 · Answer 5 · 2018-02-12 18:04:06

121

Views

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

Published on 12 Feb 2018 - 18:04

score 3.6k · Answer 6 · 2026-03-17 13:05:38

3.6k

Views

Spectrum of unitary operators lie in the unit circle

Published on 17 Mar 2026 - 13:05

score 813 · Answer 7 · 2026-03-19 15:00:31

813

Views

Hilbert space basis which is not a vector space basis

Published on 19 Mar 2026 - 15:00

score 405 · Answer 8 · 2018-02-13 16:21:58

405

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 Feb 2018 - 16:21

score 310 · Answer 9 · 2026-03-25 06:21:06

310

Views

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

Published on 25 Mar 2026 - 6:21

score 821 · Answer 10 · 2018-02-14 03:34:37

821

Views

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

Published on 14 Feb 2018 - 3:34

score 106 · Answer 11 · 2018-02-14 09:00:17

106

Views

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

Published on 14 Feb 2018 - 9:00

score 88 · Answer 12 · 2026-03-23 07:23:08

88

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 23 Mar 2026 - 7:23

score 61 · Answer 13 · 2018-02-14 12:48:35

61

Views

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

Published on 14 Feb 2018 - 12:48

score 381 · Answer 14 · 2018-02-16 19:03:58

381

Views

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

Published on 16 Feb 2018 - 19:03

score 163 · Answer 15 · 2018-02-17 14:24:07

163

Views

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

Published on 17 Feb 2018 - 14:24

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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