Question

If every absolutely convergent series is convergent in $X$, then $X$ is a Banach space.

score 312 · Answer 1 · 2018-11-16 23:34:49

312

Views

If every absolutely convergent series is convergent in $X$, then $X$ is a Banach space.

Published on 16 Nov 2018 - 23:34

score 384 · Answer 2 · 2026-03-26 06:31:14

384

Views

Is Banach fixed point theorem a necessary and sufficient condition for the existence of a fixed point

Published on 26 Mar 2026 - 6:31

score 124 · Answer 3 · 2018-11-17 10:58:46

124

Views

Show that $\forall y \in X$ the equation $x= y + Tx$ has a unique solution

Published on 17 Nov 2018 - 10:58

score 49 · Answer 4 · 2018-11-18 16:24:09

49

Views

Is the Banach space $M_{n\times n} (\mathbb{C})$ with normal structure?

Published on 18 Nov 2018 - 16:24

score 1.8k · Answer 5 · 2018-11-20 00:53:43

1.8k

Views

The limit of a strongly convergent sequence of linear bounded operators from a Banach space to a normed space

Published on 20 Nov 2018 - 0:53

score 129 · Answer 6 · 2018-11-21 11:03:23

129

Views

A closed convex set in a complex Banach space.

Published on 21 Nov 2018 - 11:03

score 302 · Answer 7 · 2018-11-22 09:32:55

302

Views

convex cone in complex Banach space

Published on 22 Nov 2018 - 9:32

score 57 · Answer 8 · 2018-11-22 19:37:01

57

Views

Is it v1,v2,v3,.. converging sequence of space $\mathbb{E}$?

Published on 22 Nov 2018 - 19:37

score 57 · Answer 9 · 2018-11-23 06:59:33

57

Views

Banach space convergence

Published on 23 Nov 2018 - 6:59

score 56 · Answer 10 · 2026-03-25 11:19:16

56

Views

Banach space with subset whose elements are at least $d\gt 0$ far from each other is not separable

Published on 25 Mar 2026 - 11:19

score 955 · Answer 11 · 2018-11-24 11:55:32

955

Views

Dense subset of two Banach spaces also dense in the intersection

Published on 24 Nov 2018 - 11:55

score 199 · Answer 12 · 2026-03-26 16:57:19

199

Views

A Banach space with a cone's order

Published on 26 Mar 2026 - 16:57

score 68 · Answer 13 · 2018-11-25 12:25:36

68

Views

Showing that the equation $x_i - \sum_{j=1}^\infty a_{ij}x_j = b_i$ has a unique solution.

Published on 25 Nov 2018 - 12:25

score 1.4k · Answer 14 · 2018-11-25 15:01:40

1.4k

Views

Set of all sequences converging to $0$ forms a Banach Space.

Published on 25 Nov 2018 - 15:01

score 455 · Answer 15 · 2018-11-25 15:52:36

455

Views

Proving that $Y= \{x_n \in \ell^2 : x_{2n} =0, n \in \mathbb N\}$ is closed and finding $Y^\bot$.

Published on 25 Nov 2018 - 15:52

List Question

If every absolutely convergent series is convergent in $X$, then $X$ is a Banach space.

Is Banach fixed point theorem a necessary and sufficient condition for the existence of a fixed point

Show that $\forall y \in X$ the equation $x= y + Tx$ has a unique solution

Is the Banach space $M_{n\times n} (\mathbb{C})$ with normal structure?

The limit of a strongly convergent sequence of linear bounded operators from a Banach space to a normed space

A closed convex set in a complex Banach space.

convex cone in complex Banach space

Is it v1,v2,v3,.. converging sequence of space $\mathbb{E}$?

Banach space convergence

Banach space with subset whose elements are at least $d\gt 0$ far from each other is not separable

Dense subset of two Banach spaces also dense in the intersection

A Banach space with a cone's order

Showing that the equation $x_i - \sum_{j=1}^\infty a_{ij}x_j = b_i$ has a unique solution.

Set of all sequences converging to $0$ forms a Banach Space.

Proving that $Y= \{x_n \in \ell^2 : x_{2n} =0, n \in \mathbb N\}$ is closed and finding $Y^\bot$.

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