Question

Subset of metric space is bounded and closed but not compact.

score 412 · Answer 1 · 2018-06-02 15:09:31

412

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Subset of metric space is bounded and closed but not compact.

Published on 02 Jun 2018 - 15:09

score 89 · Answer 2 · 2018-06-02 22:57:36

89

Views

For $p\neq q$ and $p,q\geq 1$, $L^p\neq L^q$

Published on 02 Jun 2018 - 22:57

score 158 · Answer 3 · 2018-06-05 12:32:55

158

Views

How to verify that $e^{x(z_1+1+z_2)}\frac{\Gamma (z_2) \Gamma (z_1)}{\Gamma (z_1+z_2 + 2)} \in L^1(\mathbb{R^2})$?

Published on 05 Jun 2018 - 12:32

score 256 · Answer 4 · 2026-03-25 00:01:10

256

Views

Corollary of Holder inequality

Published on 25 Mar 2026 - 0:01

score 101 · Answer 5 · 2018-06-06 04:02:31

101

Views

An operator on $\ell^2(\mathbb N)$ is restricted to $\ell^1(\mathbb N)$. What happens to the corresponding operator norms?

Published on 06 Jun 2018 - 4:02

score 110 · Answer 6 · 2018-06-06 04:58:28

110

Views

Example of a bounded operator on $\ell^2$ that does not preserve $\ell^1$?

Published on 06 Jun 2018 - 4:58

score 92 · Answer 7 · 2018-06-06 09:35:18

92

Views

An $L^p$-bounded martingale that is not $L^{p+\epsilon}$-bounded

Published on 06 Jun 2018 - 9:35

score 1.2k · Answer 8 · 2026-03-25 18:48:09

1.2k

Views

Convergence in distribution implies convergence of $L^p$ norms under additional assumption

Published on 25 Mar 2026 - 18:48

score 734 · Answer 9 · 2018-06-08 08:51:27

734

Views

Splitting up an infinite sum

Published on 08 Jun 2018 - 8:51

score 44 · Answer 10 · 2018-06-09 09:32:05

44

Views

Does $f$ periodic and continuous over $\Bbb R$ not imply that it is $L^p(0,T)\ \forall p\in[1,\infty]$ and the Fourier series converges a.e.?

Published on 09 Jun 2018 - 9:32

score 54 · Answer 11 · 2018-06-09 16:35:22

54

Views

Is there an example of a function that is $L^{p_2}$ but not $L^{p_1}$ and not $L^{p_3}$?

Published on 09 Jun 2018 - 16:35

score 1.7k · Answer 12 · 2018-06-10 05:38:40

1.7k

Views

Which of these subsets are dense in $l^2$?

Published on 10 Jun 2018 - 5:38

score 205 · Answer 13 · 2018-06-10 06:21:09

205

Views

Problem about convergence of sequence of partial sums of Fourier series

Published on 10 Jun 2018 - 6:21

score 55 · Answer 14 · 2018-06-10 18:06:41

55

Views

If $f_n \to f$ in $\|\cdot\|$, then $\|f_n\| \to \|f\|$. When is the converse true?

Published on 10 Jun 2018 - 18:06

score 60 · Answer 15 · 2018-06-11 13:02:39

60

Views

How to show that the following set is compact.

Published on 11 Jun 2018 - 13:02

List Question

Subset of metric space is bounded and closed but not compact.

For $p\neq q$ and $p,q\geq 1$, $L^p\neq L^q$

How to verify that $e^{x(z_1+1+z_2)}\frac{\Gamma (z_2) \Gamma (z_1)}{\Gamma (z_1+z_2 + 2)} \in L^1(\mathbb{R^2})$?

Corollary of Holder inequality

An operator on $\ell^2(\mathbb N)$ is restricted to $\ell^1(\mathbb N)$. What happens to the corresponding operator norms?

Example of a bounded operator on $\ell^2$ that does not preserve $\ell^1$?

An $L^p$-bounded martingale that is not $L^{p+\epsilon}$-bounded

Convergence in distribution implies convergence of $L^p$ norms under additional assumption

Splitting up an infinite sum

Does $f$ periodic and continuous over $\Bbb R$ not imply that it is $L^p(0,T)\ \forall p\in[1,\infty]$ and the Fourier series converges a.e.?

Is there an example of a function that is $L^{p_2}$ but not $L^{p_1}$ and not $L^{p_3}$?

Which of these subsets are dense in $l^2$?

Problem about convergence of sequence of partial sums of Fourier series

If $f_n \to f$ in $\|\cdot\|$, then $\|f_n\| \to \|f\|$. When is the converse true?

How to show that the following set is compact.

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