Question

Showing that a serie $\sum_n s_n$ is absolute convergent if, and only if, $\sum_n s_nt_n$ is convergent for any $(t_n)_n$ that converges to $0$

score 46 · Answer 1 · 2018-06-09 19:22:58

46

Views

Showing that a serie $\sum_n s_n$ is absolute convergent if, and only if, $\sum_n s_nt_n$ is convergent for any $(t_n)_n$ that converges to $0$

Published on 09 Jun 2018 - 19:22

score 87 · Answer 2 · 2018-06-10 11:03:14

A separable Banach space has a countable set of functionals such that for all $x\in\mathbf{B}$, $f(x)\neq 0$ for infinitely many $f$s

score 51 · Answer 3 · 2026-03-25 09:26:32

51

Views

Extending Fredholm Alternative on Banach Spaces to $\mathbb{R}$

Published on 25 Mar 2026 - 9:26

score 212 · Answer 4 · 2018-06-12 10:46:05

212

Views

Show that T is bounded.

Published on 12 Jun 2018 - 10:46

score 41 · Answer 5 · 2018-06-12 13:05:26

41

Views

Existence of extreme point $x^$ of $B_{E^}$ 'closed' to $y^*$ that norms at $u$?

Published on 12 Jun 2018 - 13:05

score 89 · Answer 6 · 2026-03-25 09:24:38

89

Views

Compactness of operators and norming sets

Published on 25 Mar 2026 - 9:24

score 48 · Answer 7 · 2018-06-13 05:53:21

48

Views

Is the map $t \mapsto (1-t)x + ty$ where $x,y$ in a Banach space a homeomorphism?

Published on 13 Jun 2018 - 5:53

score 168 · Answer 8 · 2026-03-23 03:52:16

168

Views

Example on $X^$ is reflexive but $\sigma(X^,X)\neq\sigma(X^*,X^{**})$ for a normed space $X$.

Published on 23 Mar 2026 - 3:52

score 75 · Answer 9 · 2018-06-13 23:17:26

75

Views

Show that $T$ is $w$-continuous.

Published on 13 Jun 2018 - 23:17

score 205 · Answer 10 · 2018-06-14 13:49:42

205

Views

Find a closed subspace $M$ and a non-closed subspace $N$ of a Banach space $\mathbf{B}$ such that $M\oplus N=\mathbf{B}$

Published on 14 Jun 2018 - 13:49

score 99 · Answer 11 · 2026-03-22 17:45:39

99

Views

A direct example on $X^$ is reflexive but the weak topology and weak topology on $X^*$ are not equal for a normed space $X$.

Published on 22 Mar 2026 - 17:45

score 616 · Answer 12 · 2018-06-19 03:17:40

616

Views

Countable dimensional normed space incomplete

Published on 19 Jun 2018 - 3:17

score 40 · Answer 13 · 2018-06-19 15:33:01

40

Views

Is $|f(y_1)-f(y_2)|\leqslant||f||||y_1-y_2||$ true in a Banach space?

Published on 19 Jun 2018 - 15:33

score 711 · Answer 14 · 2018-06-22 14:36:04

711

Views

Linear subspace of codimension one in infinite dimensional Banach space

Published on 22 Jun 2018 - 14:36

score 81 · Answer 15 · 2018-06-23 07:57:36

81

Views

How to prove the existence of an element of the dual of a Banach space $X$

Published on 23 Jun 2018 - 7:57

List Question

Showing that a serie $\sum_n s_n$ is absolute convergent if, and only if, $\sum_n s_nt_n$ is convergent for any $(t_n)_n$ that converges to $0$

A separable Banach space has a countable set of functionals such that for all $x\in\mathbf{B}$, $f(x)\neq 0$ for infinitely many $f$s

Extending Fredholm Alternative on Banach Spaces to $\mathbb{R}$

Show that T is bounded.

Existence of extreme point $x^$ of $B_{E^}$ 'closed' to $y^*$ that norms at $u$?

Compactness of operators and norming sets

Is the map $t \mapsto (1-t)x + ty$ where $x,y$ in a Banach space a homeomorphism?

Example on $X^$ is reflexive but $\sigma(X^,X)\neq\sigma(X^*,X^{**})$ for a normed space $X$.

Show that $T$ is $w$-continuous.

Find a closed subspace $M$ and a non-closed subspace $N$ of a Banach space $\mathbf{B}$ such that $M\oplus N=\mathbf{B}$

A direct example on $X^$ is reflexive but the weak topology and weak topology on $X^*$ are not equal for a normed space $X$.

Countable dimensional normed space incomplete

Is $|f(y_1)-f(y_2)|\leqslant||f||||y_1-y_2||$ true in a Banach space?

Linear subspace of codimension one in infinite dimensional Banach space

How to prove the existence of an element of the dual of a Banach space $X$

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