Question

Prove if $X$ is in closed linear subspace of the Hilbert space $L^{2}(\Omega, \mathcal{F}, P)$, then $X_{+}$ is also in it.

score 49 · Answer 1 · 2019-04-14 20:34:09

49

Views

Prove if $X$ is in closed linear subspace of the Hilbert space $L^{2}(\Omega, \mathcal{F}, P)$, then $X_{+}$ is also in it.

Published on 14 Apr 2019 - 20:34

score 125 · Answer 2 · 2019-04-15 06:56:02

125

Views

$\dim(\ker L^*) = \dim(\operatorname{coker} L)$

Published on 15 Apr 2019 - 6:56

score 853 · Answer 3 · 2026-02-23 04:50:04

853

Views

How to apply continuous functional calculus

Published on 23 Feb 2026 - 4:50

score 536 · Answer 4 · 2026-03-27 15:19:22

536

Views

Is the Unitary Group of a Hilbert Space a Lie group?

Published on 27 Mar 2026 - 15:19

score 51 · Answer 5 · 2026-03-29 08:14:48

51

Views

Weak convergence for linear operator in Hilbert Space

Published on 29 Mar 2026 - 8:14

score 250 · Answer 6 · 2026-03-27 10:08:29

250

Views

Decomposition of self adjoint elements by positive elements

Published on 27 Mar 2026 - 10:08

score 334 · Answer 7 · 2026-03-25 12:53:09

334

Views

Orthogonal Projection in Hilbert Space to prove weak convergence

Published on 25 Mar 2026 - 12:53

score 2.2k · Answer 8 · 2019-04-18 12:46:19

2.2k

Views

Are all finite dimensional hilbert spaces isomorphic to spaces with Euclidean norms?

Published on 18 Apr 2019 - 12:46

score 305 · Answer 9 · 2019-04-18 18:11:28

305

Views

Functions as Vectors

Published on 18 Apr 2019 - 18:11

score 41 · Answer 10 · 2026-03-25 14:23:54

41

Views

If $v\in H^1(]0,1[)$, then $|v(\lambda)| \leq ||v||_{L^1(]0,1[)} + ||v'||_{L^2(]0,1[)}$

Published on 25 Mar 2026 - 14:23

score 95 · Answer 11 · 2019-04-18 20:10:20

95

Views

Boundedness from below and density of range

Published on 18 Apr 2019 - 20:10

score 259 · Answer 12 · 2019-04-18 21:00:50

259

Views

For $\langle Tx, x \rangle \geq \|x\|^2$, prove a solution exists for $Tx = y$.

Published on 18 Apr 2019 - 21:00

score 163 · Answer 13 · 2019-04-18 21:21:59

163

Views

Bounded linear operator $A$ s.t. $Ax=y$ has a least square solution for each $y$ iff the range of $A$ is closed

Published on 18 Apr 2019 - 21:21

score 173 · Answer 14 · 2026-03-26 02:57:47

173

Views

If $(e_n)_{n\geq 1}$ is total in $H$ and $\sum \| e_n - f_n \| < 1$, prove $(f_n)$ is total.

Published on 26 Mar 2026 - 2:57

score 27 · Answer 15 · 2019-04-19 15:12:33

27

Views

$L^p$-space on the circle, question about the definition

Published on 19 Apr 2019 - 15:12

List Question

Prove if $X$ is in closed linear subspace of the Hilbert space $L^{2}(\Omega, \mathcal{F}, P)$, then $X_{+}$ is also in it.

$\dim(\ker L^*) = \dim(\operatorname{coker} L)$

How to apply continuous functional calculus

Is the Unitary Group of a Hilbert Space a Lie group?

Weak convergence for linear operator in Hilbert Space

Decomposition of self adjoint elements by positive elements

Orthogonal Projection in Hilbert Space to prove weak convergence

Are all finite dimensional hilbert spaces isomorphic to spaces with Euclidean norms?

Functions as Vectors

If $v\in H^1(]0,1[)$, then $|v(\lambda)| \leq ||v||_{L^1(]0,1[)} + ||v'||_{L^2(]0,1[)}$

Boundedness from below and density of range

For $\langle Tx, x \rangle \geq \|x\|^2$, prove a solution exists for $Tx = y$.

Bounded linear operator $A$ s.t. $Ax=y$ has a least square solution for each $y$ iff the range of $A$ is closed

If $(e_n)_{n\geq 1}$ is total in $H$ and $\sum \| e_n - f_n \| < 1$, prove $(f_n)$ is total.

$L^p$-space on the circle, question about the definition

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