Question

On the proof that positive linear functionals are continuous

score 549 · Answer 1 · 2026-04-12 12:12:43

549

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On the proof that positive linear functionals are continuous

Published on 12 Apr 2026 - 12:12

score 48 · Answer 2 · 2026-04-15 20:36:23

48

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Q:The proof of theorem 5 on section 8.1 in Royden "4ed"

Published on 15 Apr 2026 - 20:36

score 76 · Answer 3 · 2026-04-16 13:19:33

76

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Is $f=0$ in $L^1$ if it were $0$ if it were in $L^2$?

Published on 16 Apr 2026 - 13:19

score 210 · Answer 4 · 2026-04-11 19:33:06

210

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$L^2$ norm and $L^{\infty}$ inequality for periodic smooth functions

Published on 11 Apr 2026 - 19:33

score 18 · Answer 5 · 2026-04-13 00:17:56

18

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If null sets in $\mathcal{A_1}$ are also null sets in $\mathcal{A_2}$, it follows that $L_p(X,\mathcal{A_1},\nu)\subset L_p(X,\mathcal{A_2},\nu)$.

Published on 13 Apr 2026 - 0:17

score 46 · Answer 6 · 2026-04-25 03:44:35

46

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Proving that $\|Af\|_p=\sup_{g\geq 0, \|g\|_q=1}\int (Af\cdot g).$

Published on 25 Apr 2026 - 3:44

score 195 · Answer 7 · 2026-04-15 07:40:23

195

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Find the unique functional on $\ell^p$, such that $\|f\| = 1$ and for a given fixed $x \in \ell^p$, we have $|f(x)| = \|x\|$, where $1<p<\infty$

Published on 15 Apr 2026 - 7:40

score 88 · Answer 8 · 2026-04-15 08:02:26

88

Views

Two implications of an operator that preserves positivity on L2

Published on 15 Apr 2026 - 8:02

score 123 · Answer 9 · 2026-04-10 20:32:06

123

Views

FLT equation and Lp space

Published on 10 Apr 2026 - 20:32

score 67 · Answer 10 · 2026-04-16 03:51:15

67

Views

It is always true that $ \int\limits_{-t_0}^{t_0} f(t)\,e^{-iwt}\,dt = 2\,\int\limits_{0}^{t_0} f(t)\,e^{-iwt}\,dt$??

Published on 16 Apr 2026 - 3:51

score 106 · Answer 11 · 2026-04-16 15:48:29

$f \in L^{p}(\mathbb{R}^n),$where $p>1,\int{f\phi}=0$ for all $\phi\in C_c(\mathbb{R}^n)$ implies $f$ vanishes almost everywhere.

score 49 · Answer 12 · 2026-04-13 20:49:48

49

Views

PDE solution depends continuously on $u_0$

Published on 13 Apr 2026 - 20:49

score 116 · Answer 13 · 2026-04-14 09:37:57

116

Views

Finite norm of sequence implies convergence of sequence?

Published on 14 Apr 2026 - 9:37

score 80 · Answer 14 · 2026-04-11 02:31:56

80

Views

Properties of $L^1([0,1]) \to \ell^\infty(\mathbb Z)$

Published on 11 Apr 2026 - 2:31

score 305 · Answer 15 · 2026-04-17 00:47:13

305

Views

Generalized Minkowski inequality for $L^p$ spaces

Published on 17 Apr 2026 - 0:47

List Question

On the proof that positive linear functionals are continuous

Q:The proof of theorem 5 on section 8.1 in Royden "4ed"

Is $f=0$ in $L^1$ if it were $0$ if it were in $L^2$?

$L^2$ norm and $L^{\infty}$ inequality for periodic smooth functions

If null sets in $\mathcal{A_1}$ are also null sets in $\mathcal{A_2}$, it follows that $L_p(X,\mathcal{A_1},\nu)\subset L_p(X,\mathcal{A_2},\nu)$.

Proving that $\|Af\|_p=\sup_{g\geq 0, \|g\|_q=1}\int (Af\cdot g).$

Find the unique functional on $\ell^p$, such that $\|f\| = 1$ and for a given fixed $x \in \ell^p$, we have $|f(x)| = \|x\|$, where $1<p<\infty$

Two implications of an operator that preserves positivity on L2

FLT equation and Lp space

It is always true that $ \int\limits_{-t_0}^{t_0} f(t)\,e^{-iwt}\,dt = 2\,\int\limits_{0}^{t_0} f(t)\,e^{-iwt}\,dt$??

$f \in L^{p}(\mathbb{R}^n),$where $p>1,\int{f\phi}=0$ for all $\phi\in C_c(\mathbb{R}^n)$ implies $f$ vanishes almost everywhere.

PDE solution depends continuously on $u_0$

Finite norm of sequence implies convergence of sequence?

Properties of $L^1([0,1]) \to \ell^\infty(\mathbb Z)$

Generalized Minkowski inequality for $L^p$ spaces

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