Question

weak topology has less open set than strong topology (in Banach spaces). Why?

score 985 · Answer 1 · 2026-04-10 10:33:55

985

Views

weak topology has less open set than strong topology (in Banach spaces). Why?

Published on 10 Apr 2026 - 10:33

score 389 · Answer 2 · 2026-04-15 15:25:11

389

Views

Linear functional $\psi:X \to \mathbb{R}$ is $W$-weakly continuous if and only if it belongs to $W$

Published on 15 Apr 2026 - 15:25

score 85 · Answer 3 · 2026-04-17 07:49:06

85

Views

Examples of elements in $(X^)^$ that are not evaluation maps

Published on 17 Apr 2026 - 7:49

score 68 · Answer 4 · 2026-04-11 01:20:20

68

Views

Is $E^{\prime\prime}$ weak*-separable for separable Banach spaces?

Published on 11 Apr 2026 - 1:20

score 169 · Answer 5 · 2026-04-12 06:57:23

169

Views

When does the continuous dual of the weak operator topology consist only of finite linear combinations of evaluations?

Published on 12 Apr 2026 - 6:57

score 81 · Answer 6 · 2026-04-14 05:43:27

81

Views

When $E$ has finite dimension, then the weak topology and the strong topologie are the same.

Published on 14 Apr 2026 - 5:43

score 342 · Answer 7 · 2026-04-09 23:53:48

342

Views

In "Analyse fonctionnelle" of Brezis, in chapter III why do we need Banach spaces ? (especially for Kakutani's theorem)

Published on 09 Apr 2026 - 23:53

score 1.2k · Answer 8 · 2026-04-16 11:10:56

1.2k

Views

Compactness / sequentially compact / reflexive space / separable spaces / weak topology

Published on 16 Apr 2026 - 11:10

score 225 · Answer 9 · 2026-04-14 16:13:31

225

Views

Space of measures has the Dunford-Pettis property?

Published on 14 Apr 2026 - 16:13

score 143 · Answer 10 · 2026-04-15 13:25:31

143

Views

If for every $e\in E\setminus\{0\},$ there exists $e^\in A$ such that $e^(e)\neq 0,$ then $A$ is weak-star dense in $E^*?$

Published on 15 Apr 2026 - 13:25

score 399 · Answer 11 · 2026-04-16 19:47:16

399

Views

Can we prove that in a convex space, Weakly closed=> weak* closed ??

Published on 16 Apr 2026 - 19:47

score 314 · Answer 12 · 2026-04-15 22:42:52

314

Views

Closed convex hull of pure states of non-unital $C^*$-algebras

Published on 15 Apr 2026 - 22:42

score 359 · Answer 13 · 2026-04-08 16:26:52

359

Views

Question about a weak*-norm continuity of a linear operator

Published on 08 Apr 2026 - 16:26

score 203 · Answer 14 · 2026-04-14 21:49:46

203

Views

For an infinite dimensional Banach space, $X^$ when given the weak topology is of the first category in itself

Published on 14 Apr 2026 - 21:49

score 129 · Answer 15 · 2026-04-13 09:18:06

129

Views

Neighborhood of zero on weak topology

Published on 13 Apr 2026 - 9:18

List Question

weak topology has less open set than strong topology (in Banach spaces). Why?

Linear functional $\psi:X \to \mathbb{R}$ is $W$-weakly continuous if and only if it belongs to $W$

Examples of elements in $(X^)^$ that are not evaluation maps

Is $E^{\prime\prime}$ weak*-separable for separable Banach spaces?

When does the continuous dual of the weak operator topology consist only of finite linear combinations of evaluations?

When $E$ has finite dimension, then the weak topology and the strong topologie are the same.

In "Analyse fonctionnelle" of Brezis, in chapter III why do we need Banach spaces ? (especially for Kakutani's theorem)

Compactness / sequentially compact / reflexive space / separable spaces / weak topology

Space of measures has the Dunford-Pettis property?

If for every $e\in E\setminus\{0\},$ there exists $e^\in A$ such that $e^(e)\neq 0,$ then $A$ is weak-star dense in $E^*?$

Can we prove that in a convex space, Weakly closed=> weak* closed ??

Closed convex hull of pure states of non-unital $C^*$-algebras

Question about a weak*-norm continuity of a linear operator

For an infinite dimensional Banach space, $X^$ when given the weak topology is of the first category in itself

Neighborhood of zero on weak topology

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