Question

With Khinchine's inequality, prove Fourier basis is unconditional in $L^{p}[0,1]$ only for $p=2$.

score 77 · Answer 1 · 2026-03-25 06:29:32

77

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With Khinchine's inequality, prove Fourier basis is unconditional in $L^{p}[0,1]$ only for $p=2$.

Published on 25 Mar 2026 - 6:29

score 173 · Answer 2 · 2026-04-02 08:18:22

173

Views

$(C^1(\mathbb T),\|\cdot\|) , \|f\|:=|f(0)|+\|f′\|_{L^2(\mathbb T)}$ is not a Banach space.

Published on 02 Apr 2026 - 8:18

score 210 · Answer 3 · 2026-03-25 18:56:33

210

Views

How can I build a fixed point argument for Nash Equilibrium in $\mathbb{L}^2$ Banach space?

Published on 25 Mar 2026 - 18:56

score 40 · Answer 4 · 2020-07-29 16:01:59

40

Views

Boundedness of operators in nested Banach spaces

Published on 29 Jul 2020 - 16:01

score 122 · Answer 5 · 2026-03-26 22:15:09

122

Views

Show that a weak-star closed subset of dual is proximinal.

Published on 26 Mar 2026 - 22:15

score 85 · Answer 6 · 2026-03-26 01:16:37

85

Views

Frechet topology finer than a given locally convex topology

Published on 26 Mar 2026 - 1:16

score 364 · Answer 7 · 2026-03-26 19:08:10

364

Views

Is $AC[a,b]$ closed in $(BV[a,b],TV)$?

Published on 26 Mar 2026 - 19:08

score 715 · Answer 8 · 2026-03-30 20:47:42

715

Views

Showing basic properties of Riemann integral

Published on 30 Mar 2026 - 20:47

score 1k · Answer 9 · 2016-07-07 13:06:11

1k

Views

A corollary of the Hahn-Banach theorem

Published on 07 Jul 2016 - 13:06

score 198 · Answer 10 · 2016-07-08 17:50:10

198

Views

Second adjoint of the canonical embedding

Published on 08 Jul 2016 - 17:50

score 216 · Answer 11 · 2026-03-27 17:40:24

216

Views

If B(X) is isomorphic to B(Y), does that mean X is isomorphic to Y (for X and Y Banach spaces)?

Published on 27 Mar 2026 - 17:40

score 72 · Answer 12 · 2026-04-02 04:21:48

72

Views

Existence of a function that fulfills an equation

Published on 02 Apr 2026 - 4:21

score 1.2k · Answer 13 · 2016-07-11 01:04:25

1.2k

Views

Question about the proof $X'$ reflexive $\Rightarrow X$ reflexive.

Published on 11 Jul 2016 - 1:04

score 88 · Answer 14 · 2016-07-11 04:35:04

88

Views

Is a reflexive space necessarily an L-embedded space?

Published on 11 Jul 2016 - 4:35

score 95 · Answer 15 · 2016-07-11 18:28:24

95

Views

If $\|e_1+e_2+\cdots+e_n\|\leq C$ for all $n$ then $(e_i)_{i=1}^n$ is uniformly equivalent to the basis of $\ell_\infty^n$?

Published on 11 Jul 2016 - 18:28

List Question

With Khinchine's inequality, prove Fourier basis is unconditional in $L^{p}[0,1]$ only for $p=2$.

$(C^1(\mathbb T),\|\cdot\|) , \|f\|:=|f(0)|+\|f′\|_{L^2(\mathbb T)}$ is not a Banach space.

How can I build a fixed point argument for Nash Equilibrium in $\mathbb{L}^2$ Banach space?

Boundedness of operators in nested Banach spaces

Show that a weak-star closed subset of dual is proximinal.

Frechet topology finer than a given locally convex topology

Is $AC[a,b]$ closed in $(BV[a,b],TV)$?

Showing basic properties of Riemann integral

A corollary of the Hahn-Banach theorem

Second adjoint of the canonical embedding

If B(X) is isomorphic to B(Y), does that mean X is isomorphic to Y (for X and Y Banach spaces)?

Existence of a function that fulfills an equation

Question about the proof $X'$ reflexive $\Rightarrow X$ reflexive.

Is a reflexive space necessarily an L-embedded space?

If $\|e_1+e_2+\cdots+e_n\|\leq C$ for all $n$ then $(e_i)_{i=1}^n$ is uniformly equivalent to the basis of $\ell_\infty^n$?

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