List questions from schauder-basis

Published on 04 Nov 2017 - 14:44

231

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Finding a Schauder basis in a countable generating subset without Zorn's lemma

Published on 03 Dec 2017 - 20:22

494

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Schauder basis $L^p(\mathbb{R})$

Published on 03 Jan 2018 - 17:48

1.9k

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Coordinate functions of Schauder basis

Published on 18 May 2012 - 16:04

15.2k

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How to prove that if a normed space has Schauder basis, then it is separable? What about the converse?

Published on 08 Feb 2013 - 7:10

86

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every basis is monotone w.r.t. an equivalent norm $\||{x} \|| = \sup_n \|S_n x\|$

Published on 19 Aug 2020 - 22:23

57

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Each natural projection for a basis has norm at least 1.

Published on 24 Aug 2020 - 13:05

91

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The projection $P_n$ is continuous on the finite-dimensional space $P_m(X)$

Published on 31 Aug 2020 - 14:24

27

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Can I affirm that if $||u_{n}||_{H}$ blow up then the projection of $u_{n}$, $||P_{W}u_{n}||_{H}$, blow up in some finite dimensional subspace W?

Published on 14 Sep 2020 - 16:07

198

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A Schauder basic sequence in $\ell^1$?

Published on 29 Sep 2020 - 11:55

41

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Generalization of the Cartesian basis in Hilbert space

Published on 11 Nov 2020 - 17:36

430

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Can all linear operators be represented as matrices? (In infinite dimension.)

Published on 21 Nov 2020 - 13:34

180

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Constructively embedding $\mathbb{Q}^\mathbb{N}$ into $\mathbb{R}$

Published on 03 Dec 2020 - 10:49

208

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Prove that if there exists an infinite linearly independent subset E, of a vector space V, then V is infinite dimensional.

Published on 15 Mar 2021 - 19:02

65

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Which Schauder bases of $F[[x]]$ have the multiplication property?

Published on 20 Mar 2021 - 18:20

List Question

Basis of $C[a,b]$

Finding a Schauder basis in a countable generating subset without Zorn's lemma

Schauder basis $L^p(\mathbb{R})$

Coordinate functions of Schauder basis

How to prove that if a normed space has Schauder basis, then it is separable? What about the converse?

every basis is monotone w.r.t. an equivalent norm $\||{x} \|| = \sup_n \|S_n x\|$

Each natural projection for a basis has norm at least 1.

The projection $P_n$ is continuous on the finite-dimensional space $P_m(X)$

Can I affirm that if $||u_{n}||_{H}$ blow up then the projection of $u_{n}$, $||P_{W}u_{n}||_{H}$, blow up in some finite dimensional subspace W?

A Schauder basic sequence in $\ell^1$?

Generalization of the Cartesian basis in Hilbert space

Can all linear operators be represented as matrices? (In infinite dimension.)

Constructively embedding $\mathbb{Q}^\mathbb{N}$ into $\mathbb{R}$

Prove that if there exists an infinite linearly independent subset E, of a vector space V, then V is infinite dimensional.

Which Schauder bases of $F[[x]]$ have the multiplication property?

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