List questions from weak-topology

Published on 08 Sep 2019 - 9:50

357

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Unit ball has empty interior in weak-star topology.

Published on 08 Sep 2019 - 21:36

1.8k

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Strong closure vs. weak-* closure

Published on 12 Sep 2019 - 15:03

56

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Trying to understand definition of weak topology on normed vector spaces

Published on 25 Mar 2026 - 12:39

63

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Proving continuity of a monotone map from a Banach space to its dual with the weak* topology

Published on 29 Sep 2019 - 19:49

279

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Metric on $M[0,1]$ the space of measures

Published on 06 Oct 2019 - 3:21

222

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Every weak*-closed subspace of the dual space of a normed space is the range of an adjoint operator

Published on 08 Oct 2019 - 14:28

59

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How to show that $\lambda\in V^{**}$ is in the image of $V$ iff it is weak-* continuous?

Published on 21 Mar 2026 - 21:54

423

Views

Weak closure of orthonormal basis in Hilbert space

Published on 15 Oct 2019 - 13:15

25

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Is $\text{ball}_{R}(X^{\ast})\cap\bigcap_{i\in I}\{x^{\ast}\in X^{\ast} | \ |x^{\ast}(x_i)|\leq r_i\}$ norm (or weak*) connected?

Published on 01 Mar 2026 - 14:17

434

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Weak closure of orthonormal basis in Hilbert space (2)

Published on 18 Oct 2019 - 20:26

84

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Does every vector space with a weak topology contain a dense subspace which is a direct sum of real lines?

Published on 02 Mar 2026 - 2:46

402

Views

Weaker and Stronger topologies (open sets, continuity and terminology)

Published on 25 Oct 2019 - 20:46

53

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The bidual of a Banach space

Published on 02 Mar 2026 - 20:48

37

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Show that : $B_1(0,L^\infty((\Omega,\mathcal{F},\mathbb{P})))$ is compact in the weak topology $\sigma(L^1,L^\infty)$.

Published on 10 Nov 2019 - 9:38

List Question

weak* - compactness

Unit ball has empty interior in weak-star topology.

Strong closure vs. weak-* closure

Trying to understand definition of weak topology on normed vector spaces

Proving continuity of a monotone map from a Banach space to its dual with the weak* topology

Metric on $M[0,1]$ the space of measures

Every weak*-closed subspace of the dual space of a normed space is the range of an adjoint operator

How to show that $\lambda\in V^{**}$ is in the image of $V$ iff it is weak-* continuous?

Weak closure of orthonormal basis in Hilbert space

Is $\text{ball}_{R}(X^{\ast})\cap\bigcap_{i\in I}\{x^{\ast}\in X^{\ast} | \ |x^{\ast}(x_i)|\leq r_i\}$ norm (or weak*) connected?

Weak closure of orthonormal basis in Hilbert space (2)

Does every vector space with a weak topology contain a dense subspace which is a direct sum of real lines?

Weaker and Stronger topologies (open sets, continuity and terminology)

The bidual of a Banach space

Show that : $B_1(0,L^\infty((\Omega,\mathcal{F},\mathbb{P})))$ is compact in the weak topology $\sigma(L^1,L^\infty)$.

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