Question

What is $\| f \|$ where $f(x)=\sum\limits_{n=1}^\infty \frac{1}{3^n} \langle x,e_n\rangle$

score 138 · Answer 1 · 2026-03-22 15:42:20

138

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What is $\| f \|$ where $f(x)=\sum\limits_{n=1}^\infty \frac{1}{3^n} \langle x,e_n\rangle$

Published on 22 Mar 2026 - 15:42

score 96 · Answer 2 · 2026-03-17 13:39:05

96

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A question about Kleinecke-Shirokov's theorem

Published on 17 Mar 2026 - 13:39

score 1.2k · Answer 3 · 2026-03-17 07:23:56

1.2k

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Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?

Published on 17 Mar 2026 - 7:23

score 611 · Answer 4 · 2026-03-24 00:50:37

611

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Inﬁnite dimensional separable Hilbert space with orthonormal basis (weak convergence of $\frac{1}{N} \sum^{N^2}_{n=1} e_n$)

Published on 24 Mar 2026 - 0:50

score 255 · Answer 5 · 2026-03-22 05:04:01

255

Views

Why $\displaystyle\lim_{n\to+\infty}x_n\otimes y_n=x\otimes y\;?$

Published on 22 Mar 2026 - 5:04

score 350 · Answer 6 · 2026-03-19 21:33:40

350

Views

Operators with infinite rank and kernel

Published on 19 Mar 2026 - 21:33

score 200 · Answer 7 · 2026-03-20 02:58:02

200

Views

Ridge Regression in Hilbert Space (RKHS)

Published on 20 Mar 2026 - 2:58

score 289 · Answer 8 · 2026-03-17 14:25:34

289

Views

Explain a proof about the norm of derivation of operators

Published on 17 Mar 2026 - 14:25

score 164 · Answer 9 · 2026-03-18 07:38:37

164

Views

Proving that a composition of bounded operator and trace class operator is trace class

Published on 18 Mar 2026 - 7:38

score 43 · Answer 10 · 2026-03-17 12:28:36

43

Views

An Hilbert subset closed and eventually compact

Published on 17 Mar 2026 - 12:28

score 122 · Answer 11 · 2018-01-22 04:09:28

122

Views

Existence of lower-frame bounds imply reconstruction: wrong proof using finite-case.

Published on 22 Jan 2018 - 4:09

score 112 · Answer 12 · 2026-03-22 09:45:21

112

Views

Existence of $v$,$\lvert\lvert v \rvert\rvert = 1$, such that $\langle Tv, Tv \rangle = \lvert\lvert T \rvert \rvert^2$

Published on 22 Mar 2026 - 9:45

score 49 · Answer 13 · 2026-03-22 05:24:24

49

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If $V$ is a subspace of $\ell^2$ that doesn't contain a sequence which has only finitely many nonzero elements, can the closure of $V$ contain it?

Published on 22 Mar 2026 - 5:24

score 360 · Answer 14 · 2018-01-22 19:17:18

360

Views

Why $\sup_{\substack{x\in E,\\ \|x\|=1}}\|Ax\|\geq\sup_{\substack{x\in E,\\ \|x\|\leq1}}\|Ax\|?$

Published on 22 Jan 2018 - 19:17

score 34 · Answer 15 · 2026-03-16 22:19:02

34

Views

why do these inequalities hold?

Published on 16 Mar 2026 - 22:19

List Question

What is $\| f \|$ where $f(x)=\sum\limits_{n=1}^\infty \frac{1}{3^n} \langle x,e_n\rangle$

A question about Kleinecke-Shirokov's theorem

Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?

Inﬁnite dimensional separable Hilbert space with orthonormal basis (weak convergence of $\frac{1}{N} \sum^{N^2}_{n=1} e_n$)

Why $\displaystyle\lim_{n\to+\infty}x_n\otimes y_n=x\otimes y\;?$

Operators with infinite rank and kernel

Ridge Regression in Hilbert Space (RKHS)

Explain a proof about the norm of derivation of operators

Proving that a composition of bounded operator and trace class operator is trace class

An Hilbert subset closed and eventually compact

Existence of lower-frame bounds imply reconstruction: wrong proof using finite-case.

Existence of $v$,$\lvert\lvert v \rvert\rvert = 1$, such that $\langle Tv, Tv \rangle = \lvert\lvert T \rvert \rvert^2$

If $V$ is a subspace of $\ell^2$ that doesn't contain a sequence which has only finitely many nonzero elements, can the closure of $V$ contain it?

Why $\sup_{\substack{x\in E,\\ \|x\|=1}}\|Ax\|\geq\sup_{\substack{x\in E,\\ \|x\|\leq1}}\|Ax\|?$

why do these inequalities hold?

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