Question

For $B=\int \lambda d E_\lambda $ and $X$ commutes with every $E_\lambda $, why $BX$ is positive and self-adjoint?

score 113 · Answer 1 · 2026-03-22 19:22:06

113

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For $B=\int \lambda d E_\lambda $ and $X$ commutes with every $E_\lambda $, why $BX$ is positive and self-adjoint?

Published on 22 Mar 2026 - 19:22

score 74 · Answer 2 · 2026-03-25 11:20:07

74

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Essential supremum with respect to spectral measure

Published on 25 Mar 2026 - 11:20

score 1k · Answer 3 · 2026-03-25 03:19:23

1k

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Eigenspace dimension of a compact operator

Published on 25 Mar 2026 - 3:19

score 1.2k · Answer 4 · 2018-04-03 06:15:57

1.2k

Views

How to extend an orthonormal set to a basis on a Hilbert space?

Published on 03 Apr 2018 - 6:15

score 527 · Answer 5 · 2018-04-05 06:01:42

527

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How to prove $\|AB\|_1\leq\|A\|_2\|B\|_2$ (Trace-class and Hilbert-Schmidt operators)

Published on 05 Apr 2018 - 6:01

score 65 · Answer 6 · 2018-04-05 10:39:27

65

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About $B(H)$ containing a embedded copy of $M_2(\mathbb{C})$

Published on 05 Apr 2018 - 10:39

score 1.7k · Answer 7 · 2018-04-05 18:22:42

1.7k

Views

How to prove that the span of $\cos((n+1/2)x)$ and $\sin(nx)$ is dense in $L^2(-\pi,\pi)$?

Published on 05 Apr 2018 - 18:22

score 1.1k · Answer 8 · 2026-03-17 16:26:01

1.1k

Views

An orthogonal basis of a Hilbert space is Schauder?

Published on 17 Mar 2026 - 16:26

score 68 · Answer 9 · 2026-03-25 03:21:26

68

Views

If $-A \le B\le A$, can be say that the support $s(B)$ of $B$ is smaller than $s(A)$?

Published on 25 Mar 2026 - 3:21

score 93 · Answer 10 · 2026-03-25 01:14:59

93

Views

Approximations to unbounded operators

Published on 25 Mar 2026 - 1:14

score 96 · Answer 11 · 2018-04-07 22:21:24

96

Views

Separability of $L^2$

Published on 07 Apr 2018 - 22:21

score 148 · Answer 12 · 2018-04-08 21:04:23

148

Views

compact linear operator restricted to closed subspace of Hilbert space is one to one

Published on 08 Apr 2018 - 21:04

score 58 · Answer 13 · 2018-04-10 11:57:37

58

Views

Determine orthographic projection on a closed subspace

Published on 10 Apr 2018 - 11:57

score 1.1k · Answer 14 · 2018-04-10 14:52:19

1.1k

Views

Proving the infinite direct sum of orthogonal closed subspaces of a hilbert space is a closed linear subspace

Published on 10 Apr 2018 - 14:52

score 161 · Answer 15 · 2018-04-11 07:55:07

161

Views

An example of a closed bounded subset of a Hilbert space that is not totally bounded

Published on 11 Apr 2018 - 7:55

List Question

For $B=\int \lambda d E_\lambda $ and $X$ commutes with every $E_\lambda $, why $BX$ is positive and self-adjoint?

Essential supremum with respect to spectral measure

Eigenspace dimension of a compact operator

How to extend an orthonormal set to a basis on a Hilbert space?

How to prove $\|AB\|_1\leq\|A\|_2\|B\|_2$ (Trace-class and Hilbert-Schmidt operators)

About $B(H)$ containing a embedded copy of $M_2(\mathbb{C})$

How to prove that the span of $\cos((n+1/2)x)$ and $\sin(nx)$ is dense in $L^2(-\pi,\pi)$?

An orthogonal basis of a Hilbert space is Schauder?

If $-A \le B\le A$, can be say that the support $s(B)$ of $B$ is smaller than $s(A)$?

Approximations to unbounded operators

Separability of $L^2$

compact linear operator restricted to closed subspace of Hilbert space is one to one

Determine orthographic projection on a closed subspace

Proving the infinite direct sum of orthogonal closed subspaces of a hilbert space is a closed linear subspace

An example of a closed bounded subset of a Hilbert space that is not totally bounded

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