Question

Whether the following subset in the space of function is closed?

score 50 · Answer 1 · 2026-03-28 10:04:39

50

Views

Whether the following subset in the space of function is closed?

Published on 28 Mar 2026 - 10:04

score 90 · Answer 2 · 2026-03-29 13:40:59

90

Views

Can a proper subspace of a Banach space be a countable intersection of open sets?

Published on 29 Mar 2026 - 13:40

score 66 · Answer 3 · 2026-03-29 13:40:52

66

Views

Let E be a non-meager subset of a Banach space, then E - E contains a neighborhood of zero.

Published on 29 Mar 2026 - 13:40

score 228 · Answer 4 · 2026-03-27 10:10:48

228

Views

On the Fredholm Alternative for PDE's in Evan's book

Published on 27 Mar 2026 - 10:10

score 73 · Answer 5 · 2026-03-28 07:15:48

73

Views

Prove $C(X)$ is a Banach algebra by first showing for all $x$, $\vert fg(x)\vert \le \Vert f \Vert \cdot \Vert g \Vert$

Published on 28 Mar 2026 - 7:15

score 71 · Answer 6 · 2026-03-25 19:10:07

71

Views

Using Hahn-Banach theorem show that $\sum\limits_{i = 1}^{n} \alpha_i \beta_i\gt \lambda \geq \left \|\sum\limits_{i = 1}^{n} \beta_i f_i \right \|.$

Published on 25 Mar 2026 - 19:10

score 56 · Answer 7 · 2023-05-08 15:16:28

56

Views

Fake proof of weak convergence $\implies$ strong convergence

Published on 08 May 2023 - 15:16

score 156 · Answer 8 · 2023-05-11 20:23:40

156

Views

showing a functional on $l^p$ is bounded

Published on 11 May 2023 - 20:23

score 37 · Answer 9 · 2023-05-13 09:17:26

37

Views

For an extreme contraction, $T$, $\|T\pm U\|\leq 1$ implies $U=0$. How?

Published on 13 May 2023 - 9:17

score 129 · Answer 10 · 2026-03-27 03:43:10

129

Views

Conditions on Radon measure for it to be a measure of a BV function

Published on 27 Mar 2026 - 3:43

score 277 · Answer 11 · 2023-05-15 15:21:23

277

Views

Dual of continuous functions on a compact set with sup norm consists of measures

Published on 15 May 2023 - 15:21

score 92 · Answer 12 · 2026-03-27 14:10:29

92

Views

About the derivation of the Euler-Lagrange equations

Published on 27 Mar 2026 - 14:10

score 105 · Answer 13 · 2023-05-16 15:12:23

105

Views

Brezis' Exercise 5.29.2: a lemma of Grothendieck

Published on 16 May 2023 - 15:12

score 32 · Answer 14 · 2026-04-02 19:18:51

32

Views

Counterexample to Lagrange multipliers theorem in a non-Banach space?

Published on 02 Apr 2026 - 19:18

score 75 · Answer 15 · 2023-05-18 10:53:50

75

Views

Is the zero element of a Banach space the same as the zero element of a space that it is continuously embedded within?

Published on 18 May 2023 - 10:53

List Question

Whether the following subset in the space of function is closed?

Can a proper subspace of a Banach space be a countable intersection of open sets?

Let E be a non-meager subset of a Banach space, then E - E contains a neighborhood of zero.

On the Fredholm Alternative for PDE's in Evan's book

Prove $C(X)$ is a Banach algebra by first showing for all $x$, $\vert fg(x)\vert \le \Vert f \Vert \cdot \Vert g \Vert$

Using Hahn-Banach theorem show that $\sum\limits_{i = 1}^{n} \alpha_i \beta_i\gt \lambda \geq \left \|\sum\limits_{i = 1}^{n} \beta_i f_i \right \|.$

Fake proof of weak convergence $\implies$ strong convergence

showing a functional on $l^p$ is bounded

For an extreme contraction, $T$, $\|T\pm U\|\leq 1$ implies $U=0$. How?

Conditions on Radon measure for it to be a measure of a BV function

Dual of continuous functions on a compact set with sup norm consists of measures

About the derivation of the Euler-Lagrange equations

Brezis' Exercise 5.29.2: a lemma of Grothendieck

Counterexample to Lagrange multipliers theorem in a non-Banach space?

Is the zero element of a Banach space the same as the zero element of a space that it is continuously embedded within?

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