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(more) how to prove $C[-1,1]$ with $L^1$-norm is not complete

score 1.2k · Answer 1 · 2026-04-15 07:01:48

1.2k

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(more) how to prove $C[-1,1]$ with $L^1$-norm is not complete

Published on 15 Apr 2026 - 7:01

score 842 · Answer 2 · 2026-03-28 10:16:45

842

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Convergence in $L^p$ implies convergence of weak derivative

Published on 28 Mar 2026 - 10:16

score 85 · Answer 3 · 2026-04-15 20:47:46

85

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$x=\lim_{i \to \infty}e_i$ is a sequence which is not convergent, so $x\notin c_0$, then why {$e_i$}$_{i=1}^\infty$ is a Schauder basis for $c_0$?

Published on 15 Apr 2026 - 20:47

score 1.2k · Answer 4 · 2026-04-26 10:47:14

1.2k

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$L^p$ spaces between Riemannian Manifolds

Published on 26 Apr 2026 - 10:47

score 339 · Answer 5 · 2026-04-13 16:12:07

339

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Completeness of $L^p$ space

Published on 13 Apr 2026 - 16:12

score 258 · Answer 6 · 2026-04-14 21:20:51

258

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How to transform the $L^2$ inner product on a sphere $T$ into an inner product on the unit sphere $S^2$ where $\alpha T = S^2$. for $\alpha>0$?

Published on 14 Apr 2026 - 21:20

score 78 · Answer 7 · 2026-04-14 19:35:56

78

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Is $\lim_{i \to \infty}e_i$ in $ c_0$?

Published on 14 Apr 2026 - 19:35

score 1.2k · Answer 8 · 2026-04-16 22:18:36

1.2k

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If $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$ then $\|fg\|_{L^r}\leq \|f\|_{L^p}\|g\|_{L^q}$

Published on 16 Apr 2026 - 22:18

score 198 · Answer 9 · 2026-04-15 23:22:51

198

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An identity for Riemann-Stieltjes integral of $ t^p $ w.r.t. $ \alpha(t) = m(\{x:|f(x)|>t\}) $.

Published on 15 Apr 2026 - 23:22

score 294 · Answer 10 · 2026-04-17 16:00:59

294

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Prove that $\|f\|_{L^r}\leq \|f\|_{L^p}^\alpha \|f\|_{L^q}^{1-\alpha }$ if $\frac{1}{r}=\frac{\alpha }{p}+\frac{1-\alpha }{q}$

Published on 17 Apr 2026 - 16:00

score 908 · Answer 11 · 2026-04-10 20:18:08

908

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Intuition of dual space action in dual of $\ell_p$

Published on 10 Apr 2026 - 20:18

score 327 · Answer 12 · 2026-04-13 10:48:56

327

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$L^p$ norm of uniformly bounded function

Published on 13 Apr 2026 - 10:48

score 72 · Answer 13 · 2026-04-14 12:48:38

72

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On an inclusion condition between $L^p(\mathbb R)$ for different $p$ s

Published on 14 Apr 2026 - 12:48

score 175 · Answer 14 · 2026-04-11 04:57:19

175

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Convergence of expectation

Published on 11 Apr 2026 - 4:57

score 443 · Answer 15 · 2026-04-11 17:04:05

443

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Are sequences with Cesaro mean a closed subset of $\ell_\infty$?

Published on 11 Apr 2026 - 17:04

List Question

(more) how to prove $C[-1,1]$ with $L^1$-norm is not complete

Convergence in $L^p$ implies convergence of weak derivative

$x=\lim_{i \to \infty}e_i$ is a sequence which is not convergent, so $x\notin c_0$, then why {$e_i$}$_{i=1}^\infty$ is a Schauder basis for $c_0$?

$L^p$ spaces between Riemannian Manifolds

Completeness of $L^p$ space

How to transform the $L^2$ inner product on a sphere $T$ into an inner product on the unit sphere $S^2$ where $\alpha T = S^2$. for $\alpha>0$?

Is $\lim_{i \to \infty}e_i$ in $ c_0$?

If $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$ then $\|fg\|_{L^r}\leq \|f\|_{L^p}\|g\|_{L^q}$

An identity for Riemann-Stieltjes integral of $ t^p $ w.r.t. $ \alpha(t) = m(\{x:|f(x)|>t\}) $.

Prove that $\|f\|_{L^r}\leq \|f\|_{L^p}^\alpha \|f\|_{L^q}^{1-\alpha }$ if $\frac{1}{r}=\frac{\alpha }{p}+\frac{1-\alpha }{q}$

Intuition of dual space action in dual of $\ell_p$

$L^p$ norm of uniformly bounded function

On an inclusion condition between $L^p(\mathbb R)$ for different $p$ s

Convergence of expectation

Are sequences with Cesaro mean a closed subset of $\ell_\infty$?

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