Question

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

score 58 · Answer 1 · 2019-01-27 16:46:25

58

Views

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

Published on 27 Jan 2019 - 16:46

score 749 · Answer 2 · 2019-01-31 11:14:36

749

Views

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

Published on 31 Jan 2019 - 11:14

score 104 · Answer 3 · 2019-02-06 16:27:13

104

Views

Rudin's functional analysis theorem 3.21.

Published on 06 Feb 2019 - 16:27

score 1.2k · Answer 4 · 2019-02-07 10:01:40

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 07 Feb 2019 - 10:01

score 940 · Answer 5 · 2019-02-08 15:19:10

940

Views

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

Published on 08 Feb 2019 - 15:19

score 41 · Answer 6 · 2026-03-25 06:05:24

41

Views

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

Published on 25 Mar 2026 - 6:05

score 295 · Answer 7 · 2019-02-20 06:45:10

295

Views

A question on Weak and Norm topology

Published on 20 Feb 2019 - 6:45

score 258 · Answer 8 · 2019-03-08 02:17:32

258

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 08 Mar 2019 - 2:17

score 210 · Answer 9 · 2026-03-25 09:29:06

210

Views

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

Published on 25 Mar 2026 - 9:29

score 374 · Answer 10 · 2019-03-08 18:13:07

374

Views

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

Published on 08 Mar 2019 - 18:13

score 154 · Answer 11 · 2019-03-12 22:05:21

154

Views

Weak-* continuous functionals with bounded level sets

Published on 12 Mar 2019 - 22:05

score 511 · Answer 12 · 2019-03-15 11:57:45

511

Views

Weak continuity of the addition and scalar multiplication

Published on 15 Mar 2019 - 11:57

score 89 · Answer 13 · 2019-03-19 16:02:07

89

Views

How to prove or disprove the following statement on Hausdorff topology

Published on 19 Mar 2019 - 16:02

score 89 · Answer 14 · 2019-03-20 17:56:26

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 341 · Answer 15 · 2019-03-25 02:35:24

341

Views

On weak*-sequentially completeness

Published on 25 Mar 2019 - 2:35

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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