List questions from weak-topology

Published on 17 Feb 2023 - 17:04

51

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Equivalence of weak and strong continuity for finite discrete spaces

Published on 28 Feb 2023 - 13:06

53

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Confusion regarding weak star closure

Published on 03 Mar 2023 - 17:31

233

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On bounded sets of $L^2$ the weak topology is metriziable

Published on 11 Mar 2023 - 12:26

78

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How to prove that a subspace is weakly$^*$ closed

Published on 24 Mar 2023 - 20:26

110

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Convergence of inverse operator with projections

Published on 28 Mar 2023 - 1:12

82

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Hints on showing that the sequence $\frac{1}{\#S_n}\sum_{l\in S_n}\mu\circ f^{-l},S_n\subset\mathbb{N}$ converges to $f$-invariant probability measure

Published on 29 Mar 2023 - 18:45

76

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Brezis' exercise 4.16.2

Published on 05 Apr 2023 - 12:59

68

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Brezis' exercise 4.16.3

Published on 05 Apr 2023 - 15:37

27

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$u_n \to \overline f$ in the weak topology $\sigma(L^p, L^{p'})$

Published on 06 Apr 2023 - 17:16

181

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Is it necessary to consider the case $p=1$ separately?

Published on 06 Apr 2023 - 17:53

85

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Class of transport maps is not closed in space of all measurable maps?

Published on 23 Feb 2026 - 13:46

31

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Prove that $C$ is closed in the weak$^*$ topology $\sigma(L^\infty, L^1)$

Published on 09 Apr 2023 - 19:42

39

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Prove that $v_n \xrightarrow{n\to\infty} v$ in $L^\infty (\mathbb R^d)$ w.r.t. the weak$^*$ topology $\sigma(L^\infty, L^1)$

Published on 09 Apr 2023 - 23:12

32

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There is $(u_n) \subset \mathcal C_c^{\infty} (\Omega)$ such that $u_n \to u$ a.e. and $u_n \to u$ in the weak$^*$ topology $\sigma(L^\infty, L^1)$

Published on 10 Apr 2023 - 10:15

List Question

Folland: Convergence in weak topology iff convergence in dual

Equivalence of weak and strong continuity for finite discrete spaces

Confusion regarding weak star closure

On bounded sets of $L^2$ the weak topology is metriziable

How to prove that a subspace is weakly$^*$ closed

Convergence of inverse operator with projections

Hints on showing that the sequence $\frac{1}{\#S_n}\sum_{l\in S_n}\mu\circ f^{-l},S_n\subset\mathbb{N}$ converges to $f$-invariant probability measure

Brezis' exercise 4.16.2

Brezis' exercise 4.16.3

$u_n \to \overline f$ in the weak topology $\sigma(L^p, L^{p'})$

Is it necessary to consider the case $p=1$ separately?

Class of transport maps is not closed in space of all measurable maps?

Prove that $C$ is closed in the weak$^*$ topology $\sigma(L^\infty, L^1)$

Prove that $v_n \xrightarrow{n\to\infty} v$ in $L^\infty (\mathbb R^d)$ w.r.t. the weak$^*$ topology $\sigma(L^\infty, L^1)$

There is $(u_n) \subset \mathcal C_c^{\infty} (\Omega)$ such that $u_n \to u$ a.e. and $u_n \to u$ in the weak$^*$ topology $\sigma(L^\infty, L^1)$

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