Question

How to prove a norm identity for a Banach space and its dual

score 147 · Answer 1 · 2026-03-25 19:05:36

147

Views

How to prove a norm identity for a Banach space and its dual

Published on 25 Mar 2026 - 19:05

score 81 · Answer 2 · 2020-07-16 22:13:11

81

Views

Simultaneous convergence of sequence with weak- and weak$^*$-convergent terms

Published on 16 Jul 2020 - 22:13

score 118 · Answer 3 · 2026-03-25 20:33:43

118

Views

Do diffeomorphisms between arbitrary sets extend to ordinary diffeomorphisms between open sets?

Published on 25 Mar 2026 - 20:33

score 43 · Answer 4 · 2026-03-26 14:29:30

43

Views

Let $X$ be a Banach space and $E$ a sublinear subspace . Show there exists a surjective isometry $\phi : E^* \rightarrow \overline{ E}^* $

Published on 26 Mar 2026 - 14:29

score 85 · Answer 5 · 2026-03-27 13:25:42

85

Views

Trouble proving the equality when asked to compute the operator norm $\phi : \ell^{2} \to \mathbb R$ where $\phi(x)=\sum \frac{x_{n}}{n}$

Published on 27 Mar 2026 - 13:25

score 52 · Answer 6 · 2026-03-26 14:32:02

52

Views

If a Hilbert space is linearly isometric to a Banach space, will the Banach space be a Hilbert space?

Published on 26 Mar 2026 - 14:32

score 101 · Answer 7 · 2026-03-27 11:46:58

101

Views

About the hypotheses of Schauder Theorem

Published on 27 Mar 2026 - 11:46

score 131 · Answer 8 · 2020-07-19 22:38:41

131

Views

Find a counter example that if $X$ banach space is not reflexive , the the operator doesn't have to be compact

Published on 19 Jul 2020 - 22:38

score 149 · Answer 9 · 2026-03-26 04:29:23

149

Views

the identity mapping is not open

Published on 26 Mar 2026 - 4:29

score 105 · Answer 10 · 2026-03-27 05:34:24

105

Views

Is $\mathcal{L}(V)^*$ path connected?

Published on 27 Mar 2026 - 5:34

score 72 · Answer 11 · 2026-03-27 16:17:31

72

Views

If $T\colon X \to Y$ is such that $T^\colon Y^ \to Y^*$, what does this imply about $T$?

Published on 27 Mar 2026 - 16:17

score 564 · Answer 12 · 2026-03-29 05:50:15

564

Views

In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

Published on 29 Mar 2026 - 5:50

score 139 · Answer 13 · 2020-07-22 12:40:13

139

Views

How does this function arrive while formulating the auxiliary inequality for proof of $\mathcal {L^p}$ as a metric space?

Published on 22 Jul 2020 - 12:40

score 90 · Answer 14 · 2026-03-28 08:50:03

90

Views

Cartan Differentiable calculus. Show $g(x,y)= \frac{f(x)-f(y)}{x-y}$ is differentiable at $(x_{0},x_{0})$

Published on 28 Mar 2026 - 8:50

score 154 · Answer 15 · 2020-07-24 22:41:07

154

Views

Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimension

Published on 24 Jul 2020 - 22:41

List Question

How to prove a norm identity for a Banach space and its dual

Simultaneous convergence of sequence with weak- and weak$^*$-convergent terms

Do diffeomorphisms between arbitrary sets extend to ordinary diffeomorphisms between open sets?

Let $X$ be a Banach space and $E$ a sublinear subspace . Show there exists a surjective isometry $\phi : E^* \rightarrow \overline{ E}^* $

Trouble proving the equality when asked to compute the operator norm $\phi : \ell^{2} \to \mathbb R$ where $\phi(x)=\sum \frac{x_{n}}{n}$

If a Hilbert space is linearly isometric to a Banach space, will the Banach space be a Hilbert space?

About the hypotheses of Schauder Theorem

Find a counter example that if $X$ banach space is not reflexive , the the operator doesn't have to be compact

the identity mapping is not open

Is $\mathcal{L}(V)^*$ path connected?

If $T\colon X \to Y$ is such that $T^\colon Y^ \to Y^*$, what does this imply about $T$?

In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

How does this function arrive while formulating the auxiliary inequality for proof of $\mathcal {L^p}$ as a metric space?

Cartan Differentiable calculus. Show $g(x,y)= \frac{f(x)-f(y)}{x-y}$ is differentiable at $(x_{0},x_{0})$

Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimension

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