List questions from weak-topology

Published on 14 Apr 2020 - 21:35

158

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If $H$ Hilbert and $(P_k)$ is a sequence of orthogonal projections in $B(H)$, then $0$ is in weak closure of $\{\sqrt{k}P_k:k\in\mathbb{N}\}$

Published on 16 Apr 2020 - 20:26

205

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Open set is unbounded

Published on 19 Apr 2020 - 12:43

152

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Proving that a function is weakly lower semi continuous

Published on 23 Feb 2026 - 10:00

689

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Why is the ultraweak topology on $B(H)$ called "ultraweak" while it is stronger than the weak topology?

Published on 21 Apr 2020 - 18:52

75

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$ \cap_{p}\overline{\text{co}}\cup_{m\geq p}\frac{1}{m}\sum_{n=1}^{m}{C_n}\subset \cap_{p}\overline{\text{co}}\cup_{m\geq p}{C_m} $

Published on 24 Apr 2020 - 0:48

44

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Can we say that: $ cl\big(\text{co}\cup_{k\geq n}{\frac{1}{k}A}\big) $ is weak compact?

Published on 25 Mar 2026 - 14:36

238

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The dual of $\mathcal{L}_{\mathbb{R}}^{1}$ is $\mathcal{L}_{\mathbb{R}}^{\infty}$?

Published on 26 Apr 2020 - 3:19

151

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Weakest topology that makes the interval $(a,b]$ open

Published on 26 Apr 2020 - 4:06

87

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Prove that $T(E)$ is finite dimensional.

Published on 27 Apr 2020 - 4:26

64

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Weak limit points of an $L^1$-space

Published on 30 Apr 2020 - 6:25

484

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Textbook recommendations for weak topology

Published on 05 May 2020 - 9:08

625

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The Relationship between Reflexive Space, Separable Space and Compactness

Published on 23 Feb 2026 - 4:35

65

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What exactly is the relationship between weak* convergence and sequential convergence?

Published on 31 May 2020 - 5:39

55

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$ \frac{1}{n}\sum_{i=1}^{n}{C_i}\text{ is weakly compact} $

Published on 02 Jun 2020 - 0:40

List Question

Show that : $ \|A\|=\sup_{x^\in B^}{s(x^*|A)} $

If $H$ Hilbert and $(P_k)$ is a sequence of orthogonal projections in $B(H)$, then $0$ is in weak closure of $\{\sqrt{k}P_k:k\in\mathbb{N}\}$

Open set is unbounded

Proving that a function is weakly lower semi continuous

Why is the ultraweak topology on $B(H)$ called "ultraweak" while it is stronger than the weak topology?

$ \cap_{p}\overline{\text{co}}\cup_{m\geq p}\frac{1}{m}\sum_{n=1}^{m}{C_n}\subset \cap_{p}\overline{\text{co}}\cup_{m\geq p}{C_m} $

Can we say that: $ cl\big(\text{co}\cup_{k\geq n}{\frac{1}{k}A}\big) $ is weak compact?

The dual of $\mathcal{L}_{\mathbb{R}}^{1}$ is $\mathcal{L}_{\mathbb{R}}^{\infty}$?

Weakest topology that makes the interval $(a,b]$ open

Prove that $T(E)$ is finite dimensional.

Weak limit points of an $L^1$-space

Textbook recommendations for weak topology

The Relationship between Reflexive Space, Separable Space and Compactness

What exactly is the relationship between weak* convergence and sequential convergence?

$ \frac{1}{n}\sum_{i=1}^{n}{C_i}\text{ is weakly compact} $

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