Question

example of a Banach space X and a subspace Y such that Y is strongly closed but not wealky closed.

score 61 · Answer 1 · 2026-04-13 20:01:37

61

Views

example of a Banach space X and a subspace Y such that Y is strongly closed but not wealky closed.

Published on 13 Apr 2026 - 20:01

score 752 · Answer 2 · 2026-04-10 00:45:04

752

Views

Literature on relationship between strong and weak* (weak star) convergence

Published on 10 Apr 2026 - 0:45

score 107 · Answer 3 · 2026-04-14 03:14:12

107

Views

Rudin's functional analysis theorem 3.21.

Published on 14 Apr 2026 - 3:14

score 1.2k · Answer 4 · 2026-04-14 04:30:00

1.2k

Views

If $Y\subset X$ are Banach spaces such that $Y$ is dense in $X$, is it true that $X'$ is dense in $Y'$?

Published on 14 Apr 2026 - 4:30

score 942 · Answer 5 · 2026-04-14 23:45:05

942

Views

Unit ball of $X^{**}$ is weakly compact!

Published on 14 Apr 2026 - 23:45

score 43 · Answer 6 · 2026-04-14 01:32:20

43

Views

Weak-continuity of an operator on the vector space of measures

Published on 14 Apr 2026 - 1:32

score 300 · Answer 7 · 2026-04-17 08:48:03

300

Views

A question on Weak and Norm topology

Published on 17 Apr 2026 - 8:48

score 261 · Answer 8 · 2026-04-15 11:20:15

261

Views

$+:X\times X\to X,(x,y)\mapsto +(x,y)=x+y$ and $\cdot:\Bbb{R}\times X\to X,(\lambda,x)\mapsto \cdot(\lambda,y)=\lambda\cdot x$ are weakly continuous

Published on 15 Apr 2026 - 11:20

score 215 · Answer 9 · 2026-05-10 10:38:30

215

Views

Show that $g_n(x)=ne^{-nx}$ is bounded, where $x\in\Omega=]0,1[$ for $n\in\Bbb{N}.$

Published on 10 May 2026 - 10:38

score 377 · Answer 10 · 2026-04-12 06:08:27

377

Views

Can you have a weakly convergent sequence of unbounded linear operators? (Example)

Published on 12 Apr 2026 - 6:08

score 157 · Answer 11 · 2026-04-12 11:42:54

157

Views

Weak-* continuous functionals with bounded level sets

Published on 12 Apr 2026 - 11:42

score 514 · Answer 12 · 2026-04-14 13:47:02

514

Views

Weak continuity of the addition and scalar multiplication

Published on 14 Apr 2026 - 13:47

score 92 · Answer 13 · 2026-04-12 15:47:17

92

Views

How to prove or disprove the following statement on Hausdorff topology

Published on 12 Apr 2026 - 15:47

score 92 · Answer 14 · 2026-04-17 16:03:06

Prove that the If $G(f)$ inherits the product topology from $X \times Y$, then $X$ is homeomorphic to $G(f)$ via the map $x \to (x,f(x))$.

score 344 · Answer 15 · 2026-04-13 23:58:10

344

Views

On weak*-sequentially completeness

Published on 13 Apr 2026 - 23:58

List Question

example of a Banach space X and a subspace Y such that Y is strongly closed but not wealky closed.

Literature on relationship between strong and weak* (weak star) convergence

Rudin's functional analysis theorem 3.21.

If $Y\subset X$ are Banach spaces such that $Y$ is dense in $X$, is it true that $X'$ is dense in $Y'$?

Unit ball of $X^{**}$ is weakly compact!

Weak-continuity of an operator on the vector space of measures

A question on Weak and Norm topology

$+:X\times X\to X,(x,y)\mapsto +(x,y)=x+y$ and $\cdot:\Bbb{R}\times X\to X,(\lambda,x)\mapsto \cdot(\lambda,y)=\lambda\cdot x$ are weakly continuous

Show that $g_n(x)=ne^{-nx}$ is bounded, where $x\in\Omega=]0,1[$ for $n\in\Bbb{N}.$

Can you have a weakly convergent sequence of unbounded linear operators? (Example)

Weak-* continuous functionals with bounded level sets

Weak continuity of the addition and scalar multiplication

How to prove or disprove the following statement on Hausdorff topology

Prove that the If $G(f)$ inherits the product topology from $X \times Y$, then $X$ is homeomorphic to $G(f)$ via the map $x \to (x,f(x))$.

On weak*-sequentially completeness

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