Question

Understanding two representations of the inner product between elements of the form $f:\prod_k H_k\to\mathbb{C}$ for Hilbert spaces $H_k$ (e.g. $L^2$)

score 42 · Answer 1 · 2026-04-11 17:26:43

42

Views

Understanding two representations of the inner product between elements of the form $f:\prod_k H_k\to\mathbb{C}$ for Hilbert spaces $H_k$ (e.g. $L^2$)

Published on 11 Apr 2026 - 17:26

score 43 · Answer 2 · 2026-03-27 22:57:36

43

Views

Showing that if $P\in\mathcal{B}(\mathcal{H}):||P||\leq 1$ and $P$ is a projection mapping, then $P$ is necessarily an orthogonal projection

Published on 27 Mar 2026 - 22:57

score 194 · Answer 3 · 2026-04-08 03:57:46

194

Views

About the definition of direct sum of Hilbert spaces

Published on 08 Apr 2026 - 3:57

score 44 · Answer 4 · 2026-04-10 02:44:48

44

Views

Generalized convergence for operators on different Hilbert spaces

Published on 10 Apr 2026 - 2:44

score 55 · Answer 5 · 2023-02-09 22:46:13

55

Views

Prove that if $F$ is in the Bargmann-Fock space. Then so is $\exp\cdot F$

Published on 09 Feb 2023 - 22:46

score 117 · Answer 6 · 2026-04-12 22:46:24

117

Views

Relationship between the dimensions of $\ker T$ and $\ker T^*$

Published on 12 Apr 2026 - 22:46

score 39 · Answer 7 · 2026-04-12 16:11:33

39

Views

Let $A$ be a bounded operator on hilbert space $H$. If $\lVert A\rVert>1$, there $\exists$unit vectors $x,y$ such that $\langle Ax,y\rangle<-1$

Published on 12 Apr 2026 - 16:11

score 51 · Answer 8 · 2026-04-12 01:43:47

51

Views

What can we know about the fixed points of the action of a strongly continuos one-parameter subgroup of unitary operators?

Published on 12 Apr 2026 - 1:43

score 22 · Answer 9 · 2026-04-09 11:23:17

22

Views

Prove that $w(R_n)\le w(T\otimes S_n)$ where $S_n$ denote cyclic forward shift on $\Bbb{C}^n$, $R_n\in M_n(B(H))$ with subdiagonal entris $T$

Published on 09 Apr 2026 - 11:23

score 157 · Answer 10 · 2026-04-12 16:44:16

157

Views

If the infinite sum of the norms $||f_n||$ converges then $\sum f_n$ converges to some $f \in \mathcal{L}_2(\Omega)$

Published on 12 Apr 2026 - 16:44

score 35 · Answer 11 · 2023-02-13 22:38:05

35

Views

Local representation of the projection $\Pi\colon \mathcal S\mathcal H\to \mathbb P\mathcal H$

Published on 13 Feb 2023 - 22:38

score 131 · Answer 12 · 2026-04-12 10:37:00

131

Views

An inner product on a space $V$ can be extended to its completion

Published on 12 Apr 2026 - 10:37

score 40 · Answer 13 · 2026-04-12 22:50:45

40

Views

Convergence of net in the Hilbert space tensor product of two Hilbert spaces

Published on 12 Apr 2026 - 22:50

score 37 · Answer 14 · 2026-03-25 13:57:52

37

Views

Is $\left\{ \frac{1}{x-a\pm iw} \right\}_{a\in\mathbb R, w>0}$ dense in $L^2(\mathbb R)$?

Published on 25 Mar 2026 - 13:57

score 81 · Answer 15 · 2026-04-10 18:12:44

81

Views

Ranges square root compact operator

Published on 10 Apr 2026 - 18:12

List Question

Understanding two representations of the inner product between elements of the form $f:\prod_k H_k\to\mathbb{C}$ for Hilbert spaces $H_k$ (e.g. $L^2$)

Showing that if $P\in\mathcal{B}(\mathcal{H}):||P||\leq 1$ and $P$ is a projection mapping, then $P$ is necessarily an orthogonal projection

About the definition of direct sum of Hilbert spaces

Generalized convergence for operators on different Hilbert spaces

Prove that if $F$ is in the Bargmann-Fock space. Then so is $\exp\cdot F$

Relationship between the dimensions of $\ker T$ and $\ker T^*$

Let $A$ be a bounded operator on hilbert space $H$. If $\lVert A\rVert>1$, there $\exists$unit vectors $x,y$ such that $\langle Ax,y\rangle<-1$

What can we know about the fixed points of the action of a strongly continuos one-parameter subgroup of unitary operators?

Prove that $w(R_n)\le w(T\otimes S_n)$ where $S_n$ denote cyclic forward shift on $\Bbb{C}^n$, $R_n\in M_n(B(H))$ with subdiagonal entris $T$

If the infinite sum of the norms $||f_n||$ converges then $\sum f_n$ converges to some $f \in \mathcal{L}_2(\Omega)$

Local representation of the projection $\Pi\colon \mathcal S\mathcal H\to \mathbb P\mathcal H$

An inner product on a space $V$ can be extended to its completion

Convergence of net in the Hilbert space tensor product of two Hilbert spaces

Is $\left\{ \frac{1}{x-a\pm iw} \right\}_{a\in\mathbb R, w>0}$ dense in $L^2(\mathbb R)$?

Ranges square root compact operator

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