Question

If $X$ is finite dimensional, what is an explicit metric inducing the weak topology on $X?$

score 85 · Answer 1 · 2026-03-25 03:23:54

85

Views

If $X$ is finite dimensional, what is an explicit metric inducing the weak topology on $X?$

Published on 25 Mar 2026 - 3:23

score 53 · Answer 2 · 2026-03-22 12:14:45

53

Views

A is a Banach $∗$-algebra.

Published on 22 Mar 2026 - 12:14

score 209 · Answer 3 · 2026-03-20 15:53:11

209

Views

Norm on a bounded linear operator between Banach spaces

Published on 20 Mar 2026 - 15:53

score 531 · Answer 4 · 2018-02-09 00:03:31

531

Views

$X$ is the space of all continuous functions with the norm $||f||=\sup_{t\ge0}e^{kt}|f(t)|<\infty.$ Is $X$ a Banach space?

Published on 09 Feb 2018 - 0:03

score 35 · Answer 5 · 2026-03-25 04:42:55

35

Views

If each subseries of $\sum_{n=1}^\infty x_n$ is weakly convergent, then $\varphi\mapsto(\varphi(x_n))_{n\in\mathbb N}$ is a closed operator

Published on 25 Mar 2026 - 4:42

score 373 · Answer 6 · 2018-02-09 16:33:43

373

Views

Bounded continuous functions in $L^\infty$.

Published on 09 Feb 2018 - 16:33

score 87 · Answer 7 · 2018-02-10 15:08:22

87

Views

Question about linear bounded operator in Banach spaces.

Published on 10 Feb 2018 - 15:08

score 40 · Answer 8 · 2018-02-11 01:40:51

40

Views

Showing that the limit exists for a function in a Banach space

Published on 11 Feb 2018 - 1:40

score 38 · Answer 9 · 2018-02-11 01:43:12

38

Views

$\|T\| \neq \sup_{\|h\|=1} |\langle Th,h\rangle |$

Published on 11 Feb 2018 - 1:43

score 683 · Answer 10 · 2018-02-11 14:25:59

683

Views

Example of a non-closed subspace such that the quotient is not a Banach space

Published on 11 Feb 2018 - 14:25

score 92 · Answer 11 · 2018-02-13 23:19:06

92

Views

Mysterious Series Rearrangement/Permutation Problem

Published on 13 Feb 2018 - 23:19

score 552 · Answer 12 · 2026-03-22 22:33:44

552

Views

Mazur's theorem counterexample for the weak-$*$ topology

Published on 22 Mar 2026 - 22:33

score 200 · Answer 13 · 2026-03-20 07:25:49

200

Views

Proving an operator is surjective for Lumer-Phillips Theorem application.

Published on 20 Mar 2026 - 7:25

score 107 · Answer 14 · 2026-03-24 23:53:50

107

Views

Banach spaces, invertible operators

Published on 24 Mar 2026 - 23:53

score 53 · Answer 15 · 2018-02-14 17:53:53

53

Views

Understanding the $\sigma(X^{\ast\ast},X^\ast)$ topology

Published on 14 Feb 2018 - 17:53

List Question

If $X$ is finite dimensional, what is an explicit metric inducing the weak topology on $X?$

A is a Banach $∗$-algebra.

Norm on a bounded linear operator between Banach spaces

$X$ is the space of all continuous functions with the norm $||f||=\sup_{t\ge0}e^{kt}|f(t)|<\infty.$ Is $X$ a Banach space?

If each subseries of $\sum_{n=1}^\infty x_n$ is weakly convergent, then $\varphi\mapsto(\varphi(x_n))_{n\in\mathbb N}$ is a closed operator

Bounded continuous functions in $L^\infty$.

Question about linear bounded operator in Banach spaces.

Showing that the limit exists for a function in a Banach space

$\|T\| \neq \sup_{\|h\|=1} |\langle Th,h\rangle |$

Example of a non-closed subspace such that the quotient is not a Banach space

Mysterious Series Rearrangement/Permutation Problem

Mazur's theorem counterexample for the weak-$*$ topology

Proving an operator is surjective for Lumer-Phillips Theorem application.

Banach spaces, invertible operators

Understanding the $\sigma(X^{\ast\ast},X^\ast)$ topology

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