Question

If $E$, $\overline{E}$ are orthogonal projections such that $\mathrm{range}(\overline{E})=\overline{\mathrm{range}(E)}$, then is $E\ge\overline{E}$?

score 72 · Answer 1 · 2014-12-11 00:35:05

If $E$, $\overline{E}$ are orthogonal projections such that $\mathrm{range}(\overline{E})=\overline{\mathrm{range}(E)}$, then is $E\ge\overline{E}$?

score 3.8k · Answer 2 · 2026-03-28 11:53:27

3.8k

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Eigenvalues of Left Shift + Right Shift in $l_2([0,\infty))$

Published on 28 Mar 2026 - 11:53

score 135 · Answer 3 · 2014-12-11 17:39:11

135

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Proving an orthogonal projection of the Hilbert adjoint is just the adjoint

Published on 11 Dec 2014 - 17:39

score 78 · Answer 4 · 2014-12-11 19:24:00

78

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Subspace of a Hilbert space with a distinct inner product

Published on 11 Dec 2014 - 19:24

score 2.3k · Answer 5 · 2014-12-12 20:39:45

2.3k

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Derivative of norm in Hilbert space

Published on 12 Dec 2014 - 20:39

score 50 · Answer 6 · 2014-12-13 11:50:30

50

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Show that this operator is linear

Published on 13 Dec 2014 - 11:50

score 91 · Answer 7 · 2014-12-13 18:49:43

91

Views

Fréchet derivatives of $\sum_{n=1}^\infty x_n^2/n^3 -\sum_{n=1}^\infty x_n^4$

Published on 13 Dec 2014 - 18:49

score 482 · Answer 8 · 2026-03-25 14:23:32

482

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How to show that the operator $T(\{x_n\})=\{n x_n\}$ has closed graph?

Published on 25 Mar 2026 - 14:23

score 124 · Answer 9 · 2026-03-28 15:18:56

124

Views

Spectral Measures: Completeness

Published on 28 Mar 2026 - 15:18

score 381 · Answer 10 · 2014-12-14 23:40:01

381

Views

Norm of an operator and eigenvalues

Published on 14 Dec 2014 - 23:40

score 54 · Answer 11 · 2014-12-15 02:50:39

54

Views

Terminology for orthogonal projections

Published on 15 Dec 2014 - 2:50

score 130 · Answer 12 · 2026-03-29 13:47:01

130

Views

Am I doing this approximation correctly? (least squares method)

Published on 29 Mar 2026 - 13:47

score 79 · Answer 13 · 2014-12-15 18:56:43

79

Views

the norm of a linear operator

Published on 15 Dec 2014 - 18:56

score 393 · Answer 14 · 2026-03-26 17:33:39

393

Views

If $H$ is a one-dimensional Hilbert space then the zero representation of a C*-algebra on $H$ is irreducible.

Published on 26 Mar 2026 - 17:33

score 68 · Answer 15 · 2026-04-03 18:18:21

68

Views

For $(l^2,\|\cdot\|_2)$ and $e_n=(0,0,.,1,0,.)$ and a bounded linear functional $\Phi$ find $p\geq 1$ where $\sum_{n=1}^\infty |b_n|^p$ converges?

Published on 03 Apr 2026 - 18:18

List Question

If $E$, $\overline{E}$ are orthogonal projections such that $\mathrm{range}(\overline{E})=\overline{\mathrm{range}(E)}$, then is $E\ge\overline{E}$?

Eigenvalues of Left Shift + Right Shift in $l_2([0,\infty))$

Proving an orthogonal projection of the Hilbert adjoint is just the adjoint

Subspace of a Hilbert space with a distinct inner product

Derivative of norm in Hilbert space

Show that this operator is linear

Fréchet derivatives of $\sum_{n=1}^\infty x_n^2/n^3 -\sum_{n=1}^\infty x_n^4$

How to show that the operator $T(\{x_n\})=\{n x_n\}$ has closed graph?

Spectral Measures: Completeness

Norm of an operator and eigenvalues

Terminology for orthogonal projections

Am I doing this approximation correctly? (least squares method)

the norm of a linear operator

If $H$ is a one-dimensional Hilbert space then the zero representation of a C*-algebra on $H$ is irreducible.

For $(l^2,\|\cdot\|_2)$ and $e_n=(0,0,.,1,0,.)$ and a bounded linear functional $\Phi$ find $p\geq 1$ where $\sum_{n=1}^\infty |b_n|^p$ converges?

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