Question

Given the subspace of $L^2$ made by constant functions, characterize its orthogonal complement

score 524 · Answer 1 · 2018-11-30 10:15:58

524

Views

Given the subspace of $L^2$ made by constant functions, characterize its orthogonal complement

Published on 30 Nov 2018 - 10:15

score 759 · Answer 2 · 2018-11-30 12:47:34

759

Views

Given $\{x_n\},\ \{y_n\}$ orthonormal sequences in a Hilbert space, prove that $\lim_{n→+∞} ||x_n − y_n|| = 0$

Published on 30 Nov 2018 - 12:47

score 1k · Answer 3 · 2018-12-01 04:46:38

1k

Views

Direct sum of closed Orthogonal Subspaces

Published on 01 Dec 2018 - 4:46

score 1.4k · Answer 4 · 2018-12-02 11:20:09

1.4k

Views

Showing that $M + N$ is a closed subspace of the Hilbert $H$

Published on 02 Dec 2018 - 11:20

score 136 · Answer 5 · 2018-12-02 13:05:26

136

Views

Showing that $\bigg\| x - \sum_{k=1}^n \lambda_ke_k\bigg\| \geq \bigg\|x-\sum_{k=1}^n\langle x,e_k\rangle e_k \bigg\|$

Published on 02 Dec 2018 - 13:05

score 447 · Answer 6 · 2018-12-02 18:09:37

447

Views

Spectral radius of sum of commuting operators

Published on 02 Dec 2018 - 18:09

score 779 · Answer 7 · 2018-12-03 01:04:32

779

Views

Discuss compactness of the set of $L^2$ bounded functions

Published on 03 Dec 2018 - 1:04

score 164 · Answer 8 · 2026-03-26 13:51:37

164

Views

Uniqueness of faithful (!) tracial states on separable $C^*$-algebra

Published on 26 Mar 2026 - 13:51

score 56 · Answer 9 · 2018-12-03 15:25:28

56

Views

Image of a transformation becomes a Hilbert space !!

Published on 03 Dec 2018 - 15:25

score 351 · Answer 10 · 2018-12-03 23:10:30

351

Views

Bounded operator on weakly convergent sequence maps to weakly convergent sequence

Published on 03 Dec 2018 - 23:10

score 82 · Answer 11 · 2018-12-04 08:36:01

82

Views

Function $f$ from $L^2[0,1]$ such that $\int \limits_0^1 f(x)g(x)dx = g(0)$, where $g$ is polynomial.

Published on 04 Dec 2018 - 8:36

score 157 · Answer 12 · 2018-12-04 10:44:49

157

Views

Prove that $\sigma_T(T_1,T_2)\subset\sigma(T_1)\times\sigma(T_2)$

Published on 04 Dec 2018 - 10:44

score 166 · Answer 13 · 2018-12-04 13:12:30

166

Views

Discuss the strong and weak convergence of $B=\{u\in W_0^{1,2}(0,1):||u'||_{L^2}\le1\}$

Published on 04 Dec 2018 - 13:12

score 338 · Answer 14 · 2026-03-25 17:07:12

338

Views

Each Hilbert space of holomorphic functions on $\mathbb C$ is a reproducing kernel Hilbert space?

Published on 25 Mar 2026 - 17:07

score 174 · Answer 15 · 2026-03-28 00:50:55

174

Views

Convergence of a sequence on the unit sphere of Bahach or Hilbert space

Published on 28 Mar 2026 - 0:50

List Question

Given the subspace of $L^2$ made by constant functions, characterize its orthogonal complement

Given $\{x_n\},\ \{y_n\}$ orthonormal sequences in a Hilbert space, prove that $\lim_{n→+∞} ||x_n − y_n|| = 0$

Direct sum of closed Orthogonal Subspaces

Showing that $M + N$ is a closed subspace of the Hilbert $H$

Showing that $\bigg\| x - \sum_{k=1}^n \lambda_ke_k\bigg\| \geq \bigg\|x-\sum_{k=1}^n\langle x,e_k\rangle e_k \bigg\|$

Spectral radius of sum of commuting operators

Discuss compactness of the set of $L^2$ bounded functions

Uniqueness of faithful (!) tracial states on separable $C^*$-algebra

Image of a transformation becomes a Hilbert space !!

Bounded operator on weakly convergent sequence maps to weakly convergent sequence

Function $f$ from $L^2[0,1]$ such that $\int \limits_0^1 f(x)g(x)dx = g(0)$, where $g$ is polynomial.

Prove that $\sigma_T(T_1,T_2)\subset\sigma(T_1)\times\sigma(T_2)$

Discuss the strong and weak convergence of $B=\{u\in W_0^{1,2}(0,1):||u'||_{L^2}\le1\}$

Each Hilbert space of holomorphic functions on $\mathbb C$ is a reproducing kernel Hilbert space?

Convergence of a sequence on the unit sphere of Bahach or Hilbert space

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