Question

A non-empty, closed subset of $L^2([0,1])$ that does not contain a vector of smallest norm

score 427 · Answer 1 · 2026-04-15 03:47:41

427

Views

A non-empty, closed subset of $L^2([0,1])$ that does not contain a vector of smallest norm

Published on 15 Apr 2026 - 3:47

score 96 · Answer 2 · 2026-04-14 11:03:48

96

Views

Weak convergence in $L^p$ space

Published on 14 Apr 2026 - 11:03

score 52 · Answer 3 · 2026-04-15 20:25:04

52

Views

Find the values, $p \in [1,\infty)$, such that the sequence $f_n(x) = \frac{n^2}{(n^2+x)\,x^{\frac{1}{3}}}$ is convergent in $L^p((1,\infty),\mu)$

Published on 15 Apr 2026 - 20:25

score 80 · Answer 4 · 2026-05-10 15:09:52

80

Views

Is $f \mapsto (x\mapsto \int_0^x f\,\mathrm d\lambda)$ weak-strong continuous from $L^1([0,1])$ to $C([0,1])$?

Published on 10 May 2026 - 15:09

score 188 · Answer 5 · 2026-04-15 21:17:12

188

Views

Weak convergence of a sequence $(f_n) \subset L^2(\mathbb{R})$ and convergence of $\chi_n f_n$

Published on 15 Apr 2026 - 21:17

score 53 · Answer 6 · 2026-04-13 16:54:46

53

Views

Prove or disprove: $~\lim_{n\to \infty}\int |h_n - h|d\mu = 0$ when $h_n$ may not be non-negative.

Published on 13 Apr 2026 - 16:54

score 348 · Answer 7 · 2026-04-17 11:47:59

348

Views

Completeness of $\{ f_n : n \in \mathbb N \} \subset C[0,1]$ in $L^1[0,1]$

Published on 17 Apr 2026 - 11:47

score 51 · Answer 8 · 2026-04-09 13:10:09

51

Views

An operator on the space of compactly supported sequence does not satisfy a given property.

Published on 09 Apr 2026 - 13:10

score 130 · Answer 9 · 2026-04-13 19:45:59

130

Views

Non linear operator from $\ell^{25}$ to $\ell^{12}$.

Published on 13 Apr 2026 - 19:45

score 85 · Answer 10 · 2026-03-25 22:05:37

85

Views

Does there exist a constant $C>0$ such that for all simple functions $f$, $\int_1^\infty|f|\leq C(\int_1^\infty|f|^p)^{1/p}$?

Published on 25 Mar 2026 - 22:05

score 90 · Answer 11 · 2026-04-16 22:17:59

90

Views

If $f\in L^4[0,1]$ and $\|f\|_4\leq C\|f\|_2$, then $\|f\|_2\leq C_1\|f\|_1$

Published on 16 Apr 2026 - 22:17

score 45 · Answer 12 · 2026-04-16 01:45:35

45

Views

Determine whether a function $f$ satisfying $\int_{B_{2r}\setminus B_r}|f(x)|^3dx<Cr$, for every $r$ is $L^1(B_1)$

Published on 16 Apr 2026 - 1:45

score 199 · Answer 13 · 2026-04-14 11:02:41

199

Views

Is this operator between $\ell^{25}$ and $\ell^{12}$ continuous?

Published on 14 Apr 2026 - 11:02

score 1.2k · Answer 14 · 2026-04-14 22:53:10

1.2k

Views

Convergence in an $L^p$ space

Published on 14 Apr 2026 - 22:53

score 112 · Answer 15 · 2026-04-09 12:03:38

112

Views

Linear span of a compact set

Published on 09 Apr 2026 - 12:03

List Question

A non-empty, closed subset of $L^2([0,1])$ that does not contain a vector of smallest norm

Weak convergence in $L^p$ space

Find the values, $p \in [1,\infty)$, such that the sequence $f_n(x) = \frac{n^2}{(n^2+x)\,x^{\frac{1}{3}}}$ is convergent in $L^p((1,\infty),\mu)$

Is $f \mapsto (x\mapsto \int_0^x f\,\mathrm d\lambda)$ weak-strong continuous from $L^1([0,1])$ to $C([0,1])$?

Weak convergence of a sequence $(f_n) \subset L^2(\mathbb{R})$ and convergence of $\chi_n f_n$

Prove or disprove: $~\lim_{n\to \infty}\int |h_n - h|d\mu = 0$ when $h_n$ may not be non-negative.

Completeness of $\{ f_n : n \in \mathbb N \} \subset C[0,1]$ in $L^1[0,1]$

An operator on the space of compactly supported sequence does not satisfy a given property.

Non linear operator from $\ell^{25}$ to $\ell^{12}$.

Does there exist a constant $C>0$ such that for all simple functions $f$, $\int_1^\infty|f|\leq C(\int_1^\infty|f|^p)^{1/p}$?

If $f\in L^4[0,1]$ and $\|f\|_4\leq C\|f\|_2$, then $\|f\|_2\leq C_1\|f\|_1$

Determine whether a function $f$ satisfying $\int_{B_{2r}\setminus B_r}|f(x)|^3dx<Cr$, for every $r$ is $L^1(B_1)$

Is this operator between $\ell^{25}$ and $\ell^{12}$ continuous?

Convergence in an $L^p$ space

Linear span of a compact set

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