List questions from banach-spaces

Published on 14 May 2018 - 0:00

375

Views

Difference between topology of pointwise convergence, weak and weak$^*$ topologies

Published on 14 May 2018 - 12:14

225

Views

A polynomial map between Banach spaces is Fréchet differentiable

Published on 25 Mar 2026 - 6:51

240

Views

If over the complex numbers it is Banach, then so it is over the reals.

Published on 25 Mar 2026 - 10:57

43

Views

A formula for the isomorphism $\ell^1\to c^*$

Published on 14 May 2018 - 17:43

54

Views

Identifying duals and second duals in Banach spaces

Published on 14 May 2018 - 20:49

90

Views

About certain convergence of Cesaro means

Published on 15 May 2018 - 10:57

625

Views

Understanding the Core of an Operator or Map.

Published on 25 Mar 2026 - 1:24

1.3k

Views

Completeness of Holder Space

Published on 16 May 2018 - 21:42

248

Views

Lemma which is used on Open Mapping Theorem

Published on 16 May 2018 - 22:58

1k

Views

Proving $l^1$ and $l^\infty$ are infinite dimensional

Published on 18 May 2018 - 12:55

683

Views

Space of Linear and Bounded Operators is a Banach Space

Published on 19 May 2018 - 17:17

175

Views

$T:X\to X$ is absolutely summing if and only if $\sum_{n=1}^\infty \|Tx_n\|<\infty$ whenever $\sum_{n=1}^\infty x_n$ is unconditionally convergent.

Published on 20 May 2018 - 13:03

90

Views

$X$ be a reflexive Banach space, $M \subseteq X$ non-empty, closed and convex.

Published on 20 May 2018 - 23:28

56

Views

The dual space of $L^1_0(\mathbb{R}^n)$, the subspace of $L^1 (\mathbb{R}^n)$ functions with vanishing integral.

Published on 25 Mar 2026 - 4:59

List Question

Show that the mapping $x^\mapsto x^(x)+r$ is weak$^*$ continuous

Difference between topology of pointwise convergence, weak and weak$^*$ topologies

A polynomial map between Banach spaces is Fréchet differentiable

If over the complex numbers it is Banach, then so it is over the reals.

A formula for the isomorphism $\ell^1\to c^*$

Identifying duals and second duals in Banach spaces

About certain convergence of Cesaro means

Understanding the Core of an Operator or Map.

Completeness of Holder Space

Lemma which is used on Open Mapping Theorem

Proving $l^1$ and $l^\infty$ are infinite dimensional

Space of Linear and Bounded Operators is a Banach Space

$T:X\to X$ is absolutely summing if and only if $\sum_{n=1}^\infty \|Tx_n\|<\infty$ whenever $\sum_{n=1}^\infty x_n$ is unconditionally convergent.

$X$ be a reflexive Banach space, $M \subseteq X$ non-empty, closed and convex.

The dual space of $L^1_0(\mathbb{R}^n)$, the subspace of $L^1 (\mathbb{R}^n)$ functions with vanishing integral.

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