Question

An example which disproves $\|p(T)\|_{op} = \|p\|_\sup$ in arbitrary Banach spaces (Gelfand theory).

score 118 · Answer 1 · 2026-04-09 11:23:32

118

Views

An example which disproves $\|p(T)\|_{op} = \|p\|_\sup$ in arbitrary Banach spaces (Gelfand theory).

Published on 09 Apr 2026 - 11:23

score 67 · Answer 2 · 2026-04-15 10:13:30

67

Views

stronger variant of "$l^p$ spaces are increasing in $p$"： $\bigcup_{1\leq p\lneq q}l^p\neq l^q$

Published on 15 Apr 2026 - 10:13

score 83 · Answer 3 · 2026-04-13 01:23:37

83

Views

Fourier transform of linear combination of chracteritic functions preserves $L^2$ norm

Published on 13 Apr 2026 - 1:23

score 140 · Answer 4 · 2026-04-11 21:32:03

140

Views

Proving Continuity of a Lebesgue Integrable product of functions

Published on 11 Apr 2026 - 21:32

score 46 · Answer 5 · 2026-05-04 16:48:39

46

Views

Fourier transform has finite norm.

Published on 04 May 2026 - 16:48

score 178 · Answer 6 · 2026-04-11 13:04:05

178

Views

Can I say $L^p$ space is a convex set?

Published on 11 Apr 2026 - 13:04

score 209 · Answer 7 · 2026-04-14 10:50:34

209

Views

Best Embedding Constant for Weighted $L^p$ Space

Published on 14 Apr 2026 - 10:50

score 96 · Answer 8 · 2026-04-14 15:04:49

96

Views

Definiteness of Real Numbers versus Complex Numbers

Published on 14 Apr 2026 - 15:04

score 146 · Answer 9 · 2026-03-26 22:57:49

146

Views

Let $E$ be a Banach space and $p \in (1, \infty)$. Is $L_{p}(X, \mu, E)$ uniformly convex?

Published on 26 Mar 2026 - 22:57

score 173 · Answer 10 · 2026-03-26 22:55:36

173

Views

Let $E$ be a Banach space, $p \in (1, \infty)$, and $L_p := L_{p}(X, \mu, E)$. Is $(L_p)^* \cong L_{p'}$ where $\frac{1}{p} + \frac{1}{p'} = 1$?

Published on 26 Mar 2026 - 22:55

score 85 · Answer 11 · 2026-04-11 17:04:05

85

Views

Let $E$ be a Hilbert space and $p \in (1, \infty)$. Then $L_p(X, \mu, E)$ is reflexive

Published on 11 Apr 2026 - 17:04

score 40 · Answer 12 · 2026-04-16 15:20:58

40

Views

Let $E$ be a Hilbert space and $p \in (1, \infty)$. Then $(L_{p'})^* = L_{p}$ with $\frac{1}{p} + \frac{1}{p'} = 1$

Published on 16 Apr 2026 - 15:20

score 127 · Answer 13 · 2026-04-16 16:57:55

127

Views

A finite measure space is separable if and only if its induced $L_1$ space is separable

Published on 16 Apr 2026 - 16:57

score 60 · Answer 14 · 2026-04-16 15:55:01

60

Views

Find an $f\in L^1([0,1])\setminus L^2([0,1])$ such that $\int_E|f(x)|\,dx\leq\sqrt{|E|}$ for all Borel $E\subset [0,1]$.

Published on 16 Apr 2026 - 15:55

score 68 · Answer 15 · 2026-04-14 22:18:01

68

Views

A $\sigma$-algebra is complete w.r.t. the metric $d_{\mu}(A, B) := \mu(A \triangle B)$

Published on 14 Apr 2026 - 22:18

List Question

An example which disproves $\|p(T)\|_{op} = \|p\|_\sup$ in arbitrary Banach spaces (Gelfand theory).

stronger variant of "$l^p$ spaces are increasing in $p$"： $\bigcup_{1\leq p\lneq q}l^p\neq l^q$

Fourier transform of linear combination of chracteritic functions preserves $L^2$ norm

Proving Continuity of a Lebesgue Integrable product of functions

Fourier transform has finite norm.

Can I say $L^p$ space is a convex set?

Best Embedding Constant for Weighted $L^p$ Space

Definiteness of Real Numbers versus Complex Numbers

Let $E$ be a Banach space and $p \in (1, \infty)$. Is $L_{p}(X, \mu, E)$ uniformly convex?

Let $E$ be a Banach space, $p \in (1, \infty)$, and $L_p := L_{p}(X, \mu, E)$. Is $(L_p)^* \cong L_{p'}$ where $\frac{1}{p} + \frac{1}{p'} = 1$?

Let $E$ be a Hilbert space and $p \in (1, \infty)$. Then $L_p(X, \mu, E)$ is reflexive

Let $E$ be a Hilbert space and $p \in (1, \infty)$. Then $(L_{p'})^* = L_{p}$ with $\frac{1}{p} + \frac{1}{p'} = 1$

A finite measure space is separable if and only if its induced $L_1$ space is separable

Find an $f\in L^1([0,1])\setminus L^2([0,1])$ such that $\int_E|f(x)|\,dx\leq\sqrt{|E|}$ for all Borel $E\subset [0,1]$.

A $\sigma$-algebra is complete w.r.t. the metric $d_{\mu}(A, B) := \mu(A \triangle B)$

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