List questions from schauder-basis

Published on 10 Apr 2026 - 20:30

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

Published on 12 Apr 2026 - 8:50

497

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

Published on 14 Apr 2026 - 10:15

1.9k

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Coordinate functions of Schauder basis

Published on 13 Apr 2026 - 14:08

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 12 Apr 2026 - 15:47

89

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

Published on 16 Apr 2026 - 12:54

59

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

Published on 15 Apr 2026 - 13:09

94

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

Published on 16 Apr 2026 - 6:10

30

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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 15 Apr 2026 - 13:33

201

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

Published on 15 Apr 2026 - 18:47

44

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Generalization of the Cartesian basis in Hilbert space

Published on 15 Apr 2026 - 22:49

433

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

Published on 12 Apr 2026 - 18:56

183

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

Published on 16 Apr 2026 - 11:04

211

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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 Apr 2026 - 21:09

68

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

Published on 13 Apr 2026 - 16:19

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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