Question

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

score 375 · Answer 1 · 2026-03-25 11:11:49

375

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

Published on 25 Mar 2026 - 11:11

score 168 · Answer 2 · 2019-03-12 22:18:50

168

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Convergence of Indicator function in weak*-topology

Published on 12 Mar 2019 - 22:18

score 1k · Answer 3 · 2019-03-14 19:20:47

1k

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Weak convergence to 0 iff bounded and pointwise convergence to 0

Published on 14 Mar 2019 - 19:20

score 106 · Answer 4 · 2026-03-26 19:02:46

106

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If $X^n$ is a Feller process, $τ_n$ is a stopping time and $h_n\to0$, why can we conclude $|X^n_{τ_n}-X^n_{τ_n+h_n}|→0$ from $|X^n_0-X^n_{h_n}|→0$?

Published on 26 Mar 2026 - 19:02

score 47 · Answer 5 · 2019-03-18 06:42:22

47

Views

Weakly convergence

Published on 18 Mar 2019 - 6:42

score 265 · Answer 6 · 2026-03-26 11:17:23

265

Views

Merging with respect to bounded uniformly continuous functions in terms of characteristic functions

Published on 26 Mar 2026 - 11:17

score 50 · Answer 7 · 2019-03-18 18:27:20

50

Views

Convergence in Probability - Random function evaluated in random argument.

Published on 18 Mar 2019 - 18:27

score 38 · Answer 8 · 2019-03-20 06:26:37

38

Views

Weak Convergence from Strong Convergence

Published on 20 Mar 2019 - 6:26

score 94 · Answer 9 · 2019-03-21 05:16:02

94

Views

Weak star convergence of Borel probability measures on a metric space

Published on 21 Mar 2019 - 5:16

score 342 · Answer 10 · 2026-03-25 11:08:12

342

Views

On weak*-sequentially completeness

Published on 25 Mar 2026 - 11:08

score 205 · Answer 11 · 2026-03-25 00:56:02

205

Views

Weakly null sequence in Banach lattices

Published on 25 Mar 2026 - 0:56

score 132 · Answer 12 · 2026-03-25 16:03:50

132

Views

$u_n$ converges weakly to $u$ $\Leftrightarrow$ $\{u_n\}$ is bounded and $\langle x^, u_n \rangle \to \langle x^, u \rangle$

Published on 25 Mar 2026 - 16:03

score 64 · Answer 13 · 2026-03-25 20:41:51

64

Views

Conclude convergence in probability from uniform convergence on a set of limiting probability 1

Published on 25 Mar 2026 - 20:41

score 117 · Answer 14 · 2019-03-29 21:17:59

117

Views

If $\text P\left[|X_n|>n^{-\alpha}\right]\to0$ as $n\to\infty$ for some $\alpha>0$, does $(X_n)_{n\in\mathbb N}$ converge in probability?

Published on 29 Mar 2019 - 21:17

score 46 · Answer 15 · 2026-03-25 12:49:54

46

Views

$X$ Banach, $u_n \to u$ and $x^_n \xrightarrow{w^} x^$ implie that $\langle x^_n, u_n\rangle \to \langle x^*,u\rangle$.

Published on 25 Mar 2026 - 12:49

List Question

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

Convergence of Indicator function in weak*-topology

Weak convergence to 0 iff bounded and pointwise convergence to 0

If $X^n$ is a Feller process, $τ_n$ is a stopping time and $h_n\to0$, why can we conclude $|X^n_{τ_n}-X^n_{τ_n+h_n}|→0$ from $|X^n_0-X^n_{h_n}|→0$?

Weakly convergence

Merging with respect to bounded uniformly continuous functions in terms of characteristic functions

Convergence in Probability - Random function evaluated in random argument.

Weak Convergence from Strong Convergence

Weak star convergence of Borel probability measures on a metric space

On weak*-sequentially completeness

Weakly null sequence in Banach lattices

$u_n$ converges weakly to $u$ $\Leftrightarrow$ $\{u_n\}$ is bounded and $\langle x^, u_n \rangle \to \langle x^, u \rangle$

Conclude convergence in probability from uniform convergence on a set of limiting probability 1

If $\text P\left[|X_n|>n^{-\alpha}\right]\to0$ as $n\to\infty$ for some $\alpha>0$, does $(X_n)_{n\in\mathbb N}$ converge in probability?

$X$ Banach, $u_n \to u$ and $x^_n \xrightarrow{w^} x^$ implie that $\langle x^_n, u_n\rangle \to \langle x^*,u\rangle$.

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