Question

Weak convergence of bounded sequence $(x_n)$ in Hilbert space where $\langle{x_n,y\rangle}\rightarrow \langle{x_n,y\rangle}$ for all $y\in D\subset H$

score 708 · Answer 1 · 2019-01-05 13:46:34

708

Views

Weak convergence of bounded sequence $(x_n)$ in Hilbert space where $\langle{x_n,y\rangle}\rightarrow \langle{x_n,y\rangle}$ for all $y\in D\subset H$

Published on 05 Jan 2019 - 13:46

score 1.2k · Answer 2 · 2026-03-26 19:25:07

1.2k

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Mercer's Theorem importance (Kernels)

Published on 26 Mar 2026 - 19:25

score 117 · Answer 3 · 2026-03-26 09:14:23

117

Views

Prove $Tx=x$, for $x\in H$, if and only if $(Tx,x)=\|x\|^2$ and $\ker(I-T)=\ker(I-T^*)$

Published on 26 Mar 2026 - 9:14

score 48 · Answer 4 · 2026-03-27 03:08:29

48

Views

Boundedness and Strong convergence

Published on 27 Mar 2026 - 3:08

score 207 · Answer 5 · 2026-03-26 12:40:10

207

Views

Reference for spectral theorem for normal operators.

Published on 26 Mar 2026 - 12:40

score 61 · Answer 6 · 2019-01-07 16:59:55

61

Views

Show an inequality

Published on 07 Jan 2019 - 16:59

score 547 · Answer 7 · 2019-01-07 18:09:25

547

Views

What is the operator norm of $Tf(x) = x^2f(x)$?

Published on 07 Jan 2019 - 18:09

score 154 · Answer 8 · 2026-03-28 08:49:31

154

Views

Real positive index Sobolev spaces are Hilbert spaces

Published on 28 Mar 2026 - 8:49

score 138 · Answer 9 · 2019-01-07 21:24:45

138

Views

show that $\ker(Id-T) = \ker(Id-T)^{\star}$

Published on 07 Jan 2019 - 21:24

score 68 · Answer 10 · 2026-03-26 09:09:17

68

Views

Prove that $(Au)(t)=\frac{d^{2}u(t)}{dt^{2}}$ is self-adjoint

Published on 26 Mar 2026 - 9:09

score 42 · Answer 11 · 2019-01-08 07:54:34

42

Views

analysis of $T : f \to Tf$ with $[T(f)](x) = ie^{i\pi x}(\int_0^x e^{-i\pi t}f(t)dt - \int_x^1 e^{-i\pi t}f(t)dt)$

Published on 08 Jan 2019 - 7:54

score 63 · Answer 12 · 2019-01-08 13:59:48

63

Views

$F(L_2([0,1],\mu))$ is dense in $L_2([0,1],\mu)$, where $F$ is the multiplication operator

Published on 08 Jan 2019 - 13:59

score 85 · Answer 13 · 2026-03-26 22:15:17

85

Views

$H$ Hilbert space, $T$ symmetric bounded linear, when is $H=R(T) \oplus N(T)$?

Published on 26 Mar 2026 - 22:15

score 1.5k · Answer 14 · 2019-01-08 20:18:02

1.5k

Views

Proof that any sequence in $\mathbb{C}^k$ converges iff each component sequence converges.

Published on 08 Jan 2019 - 20:18

score 95 · Answer 15 · 2019-01-09 15:43:46

95

Views

Spectrum of operator A

Published on 09 Jan 2019 - 15:43

List Question

Weak convergence of bounded sequence $(x_n)$ in Hilbert space where $\langle{x_n,y\rangle}\rightarrow \langle{x_n,y\rangle}$ for all $y\in D\subset H$

Mercer's Theorem importance (Kernels)

Prove $Tx=x$, for $x\in H$, if and only if $(Tx,x)=\|x\|^2$ and $\ker(I-T)=\ker(I-T^*)$

Boundedness and Strong convergence

Reference for spectral theorem for normal operators.

Show an inequality

What is the operator norm of $Tf(x) = x^2f(x)$?

Real positive index Sobolev spaces are Hilbert spaces

show that $\ker(Id-T) = \ker(Id-T)^{\star}$

Prove that $(Au)(t)=\frac{d^{2}u(t)}{dt^{2}}$ is self-adjoint

analysis of $T : f \to Tf$ with $[T(f)](x) = ie^{i\pi x}(\int_0^x e^{-i\pi t}f(t)dt - \int_x^1 e^{-i\pi t}f(t)dt)$

$F(L_2([0,1],\mu))$ is dense in $L_2([0,1],\mu)$, where $F$ is the multiplication operator

$H$ Hilbert space, $T$ symmetric bounded linear, when is $H=R(T) \oplus N(T)$?

Proof that any sequence in $\mathbb{C}^k$ converges iff each component sequence converges.

Spectrum of operator A

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