Question

How to show the Cauchy-Schwarz inequality $\langle x,y\rangle\leq \|y\|\|x\|_*$ for computing the Fenchel conjugate of a norm

score 4.3k · Answer 1 · 2026-03-25 07:45:39

4.3k

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How to show the Cauchy-Schwarz inequality $\langle x,y\rangle\leq \|y\|\|x\|_*$ for computing the Fenchel conjugate of a norm

Published on 25 Mar 2026 - 7:45

score 147 · Answer 2 · 2018-02-20 13:49:53

147

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Prove that $||(\sum^k_{i=1}|f_i|)^{\frac{1}{2}}||_p \leq (\sum^k_i ||f_i||^2_p)^{\frac{1}{2}}$

Published on 20 Feb 2018 - 13:49

score 102 · Answer 3 · 2026-03-25 09:33:49

102

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Given $T:E^\to E^,$ does there exist $S:E\to E$ such that $\langle Te^,e \rangle = \langle e^,Se\rangle?$

Published on 25 Mar 2026 - 9:33

score 49 · Answer 4 · 2018-02-20 14:55:20

49

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Consider the operator $T:l^2\to L^2(\mathbb{R})$ defined by:

Published on 20 Feb 2018 - 14:55

score 65 · Answer 5 · 2026-03-26 18:29:59

65

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Continuity of a function from norm space to R

Published on 26 Mar 2026 - 18:29

score 91 · Answer 6 · 2026-03-24 22:18:15

91

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Fourier transform, series, distribution: $F\phi=\sum_{n \in \mathbb{Z}} \phi(n), ~~~~~ \phi \in \mathcal S(\mathbb{R})$

Published on 24 Mar 2026 - 22:18

score 893 · Answer 7 · 2018-02-20 22:04:25

893

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If a normed space is finite dimensional, the unit sphere is compact

Published on 20 Feb 2018 - 22:04

score 186 · Answer 8 · 2026-03-23 06:46:16

186

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Holomorphic functional calculus proving a property of fractional powers

Published on 23 Mar 2026 - 6:46

score 493 · Answer 9 · 2026-03-25 08:07:07

493

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Measures on infinite dimensional spaces?

Published on 25 Mar 2026 - 8:07

score 151 · Answer 10 · 2026-03-26 18:40:58

151

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Show that a function $N:\mathcal Y \rightarrow \mathbb R _+$ defined by $N(y)= \left\lvert \int_a^b y(x) dx \right\rvert$ doesn't define a norm...

Published on 26 Mar 2026 - 18:40

score 182 · Answer 11 · 2018-02-21 03:17:44

182

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The orthogonal projection $P$ on $S$ is given by $P(f)=\chi_{E}f$

Published on 21 Feb 2018 - 3:17

score 138 · Answer 12 · 2026-03-24 22:12:59

138

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showing that $|u|$ is invertible whenever $u$ is in a C* algebra

Published on 24 Mar 2026 - 22:12

score 56 · Answer 13 · 2018-02-21 04:32:13

56

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$|F_{0}(z)| \leq e^{\frac{\pi}{2}}$ in unit disc, but $\lim_{r \rightarrow 1} F_{0}(r)$ does not exist.

Published on 21 Feb 2018 - 4:32

score 177 · Answer 14 · 2026-04-01 23:08:47

177

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Further questions about showing that a hyperplane is parallel to the null space of a linear functional

Published on 01 Apr 2026 - 23:08

score 147 · Answer 15 · 2026-04-02 02:19:24

147

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Intuition for compact embedding of $H^1([0,1])$ in $L^2([0,1])$?

Published on 02 Apr 2026 - 2:19

List Question

How to show the Cauchy-Schwarz inequality $\langle x,y\rangle\leq \|y\|\|x\|_*$ for computing the Fenchel conjugate of a norm

Prove that $||(\sum^k_{i=1}|f_i|)^{\frac{1}{2}}||_p \leq (\sum^k_i ||f_i||^2_p)^{\frac{1}{2}}$

Given $T:E^\to E^,$ does there exist $S:E\to E$ such that $\langle Te^,e \rangle = \langle e^,Se\rangle?$

Consider the operator $T:l^2\to L^2(\mathbb{R})$ defined by:

Continuity of a function from norm space to R

Fourier transform, series, distribution: $F\phi=\sum_{n \in \mathbb{Z}} \phi(n), ~~~~~ \phi \in \mathcal S(\mathbb{R})$

If a normed space is finite dimensional, the unit sphere is compact

Holomorphic functional calculus proving a property of fractional powers

Measures on infinite dimensional spaces?

Show that a function $N:\mathcal Y \rightarrow \mathbb R _+$ defined by $N(y)= \left\lvert \int_a^b y(x) dx \right\rvert$ doesn't define a norm...

The orthogonal projection $P$ on $S$ is given by $P(f)=\chi_{E}f$

showing that $|u|$ is invertible whenever $u$ is in a C* algebra

$|F_{0}(z)| \leq e^{\frac{\pi}{2}}$ in unit disc, but $\lim_{r \rightarrow 1} F_{0}(r)$ does not exist.

Further questions about showing that a hyperplane is parallel to the null space of a linear functional

Intuition for compact embedding of $H^1([0,1])$ in $L^2([0,1])$?

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