Question

Determine $\inf_{f \in C[0,1]} \int_0^1 t^2 \mathrm{Re}f(t)dt$ subject to certain constraints

score 61 · Answer 1 · 2026-03-26 19:20:07

61

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Determine $\inf_{f \in C[0,1]} \int_0^1 t^2 \mathrm{Re}f(t)dt$ subject to certain constraints

Published on 26 Mar 2026 - 19:20

score 1.8k · Answer 2 · 2019-11-26 23:55:17

1.8k

Views

prove a operator is unitary.

Published on 26 Nov 2019 - 23:55

score 302 · Answer 3 · 2019-11-27 01:24:44

302

Views

if bounded linear operator $T$ is positive definite,then $T$ has a bounded inverse $T^{-1}$

Published on 27 Nov 2019 - 1:24

score 608 · Answer 4 · 2019-11-27 01:59:43

608

Views

Counter Example to Minimal Norm Theorem for Hilbert Spaces

Published on 27 Nov 2019 - 1:59

score 102 · Answer 5 · 2026-03-26 19:03:03

102

Views

Why is $S\colon\ell^{2}\to\ell^{2}$ defined by $(Sx)_{m}:=\sum_{n\in\mathbb{N}}a_{m,n}x_{n}$ a compact operator?

Published on 26 Mar 2026 - 19:03

score 258 · Answer 6 · 2026-03-27 03:40:59

258

Views

The density of the range of a bounded linear operator on L2[0,1]

Published on 27 Mar 2026 - 3:40

score 205 · Answer 7 · 2019-11-28 04:43:03

205

Views

Open sets in the weak topology of a Hilbert Space

Published on 28 Nov 2019 - 4:43

score 47 · Answer 8 · 2026-03-11 06:51:53

47

Views

If $I+B$ is invertible in $l^2(\mathbb{Z})$ where $B$ is a compact opreator, is $I+B^N$ invertible where $B^N$ is a truncated version of $B$?

Published on 11 Mar 2026 - 6:51

score 114 · Answer 9 · 2026-03-31 11:29:17

114

Views

Fourier Transform and Vector Spaces

Published on 31 Mar 2026 - 11:29

score 22 · Answer 10 · 2026-03-25 12:37:38

22

Views

Optimize the contractivity of a self-adjoint operator on a closed subspace

Published on 25 Mar 2026 - 12:37

score 134 · Answer 11 · 2019-11-29 02:35:12

134

Views

Show that Toeplitz Operator is Norm-Decreasing.

Published on 29 Nov 2019 - 2:35

score 211 · Answer 12 · 2019-11-29 03:12:07

211

Views

Let $A,B \in \mathcal{B}(\mathcal{H})$ with $A$ self-adjoint and $B$ positive. Prove that if $BAB + A = 0$, then $A = 0$.

Published on 29 Nov 2019 - 3:12

score 116 · Answer 13 · 2026-03-29 05:27:23

116

Views

Consider a Hilbert Space $H$ such that $\sum_{n=0}^\infty \|x_n-y_n\| < 1.$ Show that if $z\perp y_n$ with $\forall n>0$ then $z=0$

Published on 29 Mar 2026 - 5:27

score 24 · Answer 14 · 2019-11-29 06:11:17

Show that if $(〈x_n,y〉)_{n \in \mathbb{N}}$ converges for all $y \in H$, then there is $x \in H$ such that $f(x_n) \to f(x)$ as $n \to \infty$

score 180 · Answer 15 · 2026-03-26 19:20:06

180

Views

If $H$ Hilbert, $A\colon H\to H$ bounded and $A(M)$ closed for all closed subspaces $M$, then $A(H)$ and $\ker(A)$ not both infinite dimensional?

Published on 26 Mar 2026 - 19:20

List Question

Determine $\inf_{f \in C[0,1]} \int_0^1 t^2 \mathrm{Re}f(t)dt$ subject to certain constraints

prove a operator is unitary.

if bounded linear operator $T$ is positive definite,then $T$ has a bounded inverse $T^{-1}$

Counter Example to Minimal Norm Theorem for Hilbert Spaces

Why is $S\colon\ell^{2}\to\ell^{2}$ defined by $(Sx)_{m}:=\sum_{n\in\mathbb{N}}a_{m,n}x_{n}$ a compact operator?

The density of the range of a bounded linear operator on L2[0,1]

Open sets in the weak topology of a Hilbert Space

If $I+B$ is invertible in $l^2(\mathbb{Z})$ where $B$ is a compact opreator, is $I+B^N$ invertible where $B^N$ is a truncated version of $B$?

Fourier Transform and Vector Spaces

Optimize the contractivity of a self-adjoint operator on a closed subspace

Show that Toeplitz Operator is Norm-Decreasing.

Let $A,B \in \mathcal{B}(\mathcal{H})$ with $A$ self-adjoint and $B$ positive. Prove that if $BAB + A = 0$, then $A = 0$.

Consider a Hilbert Space $H$ such that $\sum_{n=0}^\infty \|x_n-y_n\| < 1.$ Show that if $z\perp y_n$ with $\forall n>0$ then $z=0$

Show that if $(〈x_n,y〉)_{n \in \mathbb{N}}$ converges for all $y \in H$, then there is $x \in H$ such that $f(x_n) \to f(x)$ as $n \to \infty$

If $H$ Hilbert, $A\colon H\to H$ bounded and $A(M)$ closed for all closed subspaces $M$, then $A(H)$ and $\ker(A)$ not both infinite dimensional?

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