Question

A bounded positive linear mapping $T$ is an orthogonal projection if $\mathrm{dim}(\mathcal{R}(T))=1$ and $\sum_{k}\left<T(e_k),e_k\right>=1$

score 57 · Answer 1 · 2023-04-23 13:40:16

57

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A bounded positive linear mapping $T$ is an orthogonal projection if $\mathrm{dim}(\mathcal{R}(T))=1$ and $\sum_{k}\left<T(e_k),e_k\right>=1$

Published on 23 Apr 2023 - 13:40

score 32 · Answer 2 · 2026-04-12 12:37:53

32

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Is $C^\infty(U)$ a Borel subset of $L^2(U)$ when $U$ is a compact subset of $\mathbb{R}^n$?

Published on 12 Apr 2026 - 12:37

score 38 · Answer 3 · 2026-04-13 19:17:20

38

Views

Is the direct sum of Hilbert spaces a 'topological subspace' of the direct product equipped with the product topology?

Published on 13 Apr 2026 - 19:17

score 52 · Answer 4 · 2026-03-25 22:10:04

52

Views

Does the existence of an eigenbasis imply boundedness?

Published on 25 Mar 2026 - 22:10

score 65 · Answer 5 · 2026-03-25 22:05:20

65

Views

Is the kernel finite-dimensional if only finitely many basis-vectors of a Hilbert basis are mapped to zero?

Published on 25 Mar 2026 - 22:05

score 126 · Answer 6 · 2026-04-12 03:31:42

126

Views

Can we simultaneously diagonalize an uncountable family of commuting operators?

Published on 12 Apr 2026 - 3:31

score 72 · Answer 7 · 2026-04-11 16:50:18

72

Views

Hilbert Space with two inner product and showing map $T_p$ is bounded

Published on 11 Apr 2026 - 16:50

score 42 · Answer 8 · 2026-04-12 21:00:26

42

Views

Infinite series of squares of elements of orthonormal basis of $L^2(a,b)$

Published on 12 Apr 2026 - 21:00

score 79 · Answer 9 · 2026-04-12 02:17:46

79

Views

Measurable functions with range in a Hilbert space that’s not necessarily separable

Published on 12 Apr 2026 - 2:17

score 104 · Answer 10 · 2026-03-26 06:32:41

104

Views

If $x_n \to x$ and $y_n \to y$ weakly. Then $\langle x, y\rangle = \lim_n \langle x_n, y_n\rangle$

Published on 26 Mar 2026 - 6:32

score 38 · Answer 11 · 2026-03-25 09:48:31

38

Views

Can an eigenbasis be divided into bases of the eigenspaces?

Published on 25 Mar 2026 - 9:48

score 54 · Answer 12 · 2026-03-25 08:12:52

54

Views

Representation of semigroup of trace-class operators in terms of projectors

Published on 25 Mar 2026 - 8:12

score 144 · Answer 13 · 2026-04-11 17:13:21

144

Views

Are absolutely continuous functions with values in a Hilbert space differentiable almost everywhere?

Published on 11 Apr 2026 - 17:13

score 782 · Answer 14 · 2026-03-28 08:36:35

782

Views

Example of an inner product space with no orthonormal basis

Published on 28 Mar 2026 - 8:36

score 81 · Answer 15 · 2023-04-27 17:14:42

81

Views

Prove that if $t:=\lim_n t_n >0$, then $(u_n)$ converges

Published on 27 Apr 2023 - 17:14

List Question

A bounded positive linear mapping $T$ is an orthogonal projection if $\mathrm{dim}(\mathcal{R}(T))=1$ and $\sum_{k}\left<T(e_k),e_k\right>=1$

Is $C^\infty(U)$ a Borel subset of $L^2(U)$ when $U$ is a compact subset of $\mathbb{R}^n$?

Is the direct sum of Hilbert spaces a 'topological subspace' of the direct product equipped with the product topology?

Does the existence of an eigenbasis imply boundedness?

Is the kernel finite-dimensional if only finitely many basis-vectors of a Hilbert basis are mapped to zero?

Can we simultaneously diagonalize an uncountable family of commuting operators?

Hilbert Space with two inner product and showing map $T_p$ is bounded

Infinite series of squares of elements of orthonormal basis of $L^2(a,b)$

Measurable functions with range in a Hilbert space that’s not necessarily separable

If $x_n \to x$ and $y_n \to y$ weakly. Then $\langle x, y\rangle = \lim_n \langle x_n, y_n\rangle$

Can an eigenbasis be divided into bases of the eigenspaces?

Representation of semigroup of trace-class operators in terms of projectors

Are absolutely continuous functions with values in a Hilbert space differentiable almost everywhere?

Example of an inner product space with no orthonormal basis

Prove that if $t:=\lim_n t_n >0$, then $(u_n)$ converges

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