List questions from lp-spaces

123

Views

Let ${a_n}$ be in $\ell_\infty$ . Prove that $f$ defined by $f({b_n})=\sum_\infty a_nb_n$ is a continuous real valued function on $\ell_1$

Published on 21 Oct 2015 - 16:58

169

Views

Are $\ell^p$ and $L^p [0,1]$ isometric with p distinct from 2?

Published on 22 Oct 2015 - 18:21

925

Views

Reflexivity of intersection of two $L^p$ space

Published on 09 Apr 2026 - 17:13

93

Views

How could I find a non-closed linear subspace $X$ of $l^{2}$ , such that $ l^{2} \ne X + X^{\perp}?$

Published on 11 Apr 2026 - 18:05

58

Views

An inequality involving a $C^\infty$ function and its Fourier coefficients

Published on 28 Mar 2026 - 8:13

96

Views

Hölder inequality on probability space

Published on 25 Oct 2015 - 12:59

81

Views

some important density result

Published on 25 Oct 2015 - 23:11

53

Views

Deriviative estimates in finite $L^p$ space

Published on 01 Apr 2026 - 7:22

1k

Views

In the definition of an $L^p$ space, do we assume $p$ is an integer, or at least rational?

Published on 27 Oct 2015 - 2:31

72

Views

distribution space

Published on 18 Apr 2026 - 5:35

392

Views

Convergence in $L^p$ and Minkowski's inequality problem

Published on 27 Oct 2015 - 18:27

130

Views

Problem related to $L^p$ space

Published on 29 Oct 2015 - 4:02

76

Views

Splitting integrals in $L^p$

Published on 29 Oct 2015 - 6:05

843

Views

$L^p(\mathbb{R})$ separable.

Published on 09 Apr 2026 - 22:11

143

Views

$f \mapsto f(0)$ is not continuous on $L^2$

Published on 29 Oct 2015 - 7:00

List Question

Let ${a_n}$ be in $\ell_\infty$ . Prove that $f$ defined by $f({b_n})=\sum_\infty a_nb_n$ is a continuous real valued function on $\ell_1$

Are $\ell^p$ and $L^p [0,1]$ isometric with p distinct from 2?

Reflexivity of intersection of two $L^p$ space

How could I find a non-closed linear subspace $X$ of $l^{2}$ , such that $ l^{2} \ne X + X^{\perp}?$

An inequality involving a $C^\infty$ function and its Fourier coefficients

Hölder inequality on probability space

some important density result

Deriviative estimates in finite $L^p$ space

In the definition of an $L^p$ space, do we assume $p$ is an integer, or at least rational?

distribution space

Convergence in $L^p$ and Minkowski's inequality problem

Problem related to $L^p$ space

Splitting integrals in $L^p$

$L^p(\mathbb{R})$ separable.

$f \mapsto f(0)$ is not continuous on $L^2$

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