List questions from weak-topology

Published on 25 Mar 2026 - 23:37

159

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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 25 Mar 2026 - 23:42

207

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Open set is unbounded

Published on 10 May 2026 - 21:43

153

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Proving that a function is weakly lower semi continuous

Published on 09 Apr 2026 - 13:38

690

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

Published on 25 Mar 2026 - 23:38

76

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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 25 Mar 2026 - 23:42

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

239

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

Published on 25 Mar 2026 - 22:10

152

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

Published on 25 Mar 2026 - 23:37

88

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

Published on 25 Mar 2026 - 22:09

65

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

Published on 25 Mar 2026 - 22:03

485

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Textbook recommendations for weak topology

Published on 26 Mar 2026 - 1:07

626

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The Relationship between Reflexive Space, Separable Space and Compactness

Published on 09 Apr 2026 - 13:32

67

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

Published on 11 May 2026 - 1:05

56

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

Published on 25 Mar 2026 - 22:03

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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