Question

A subspace $Y$ of a Banach space $X$ is complete iff the set $Y$ is closed in $X$.

score 3.9k · Answer 1 · 2026-03-25 01:28:52

3.9k

Views

A subspace $Y$ of a Banach space $X$ is complete iff the set $Y$ is closed in $X$.

Published on 25 Mar 2026 - 1:28

score 108 · Answer 2 · 2018-03-21 21:19:50

108

Views

Non-linear functional on a Banach space

Published on 21 Mar 2018 - 21:19

score 53 · Answer 3 · 2026-03-25 06:06:58

53

Views

(From Royden 3rd Ed )How to prove the delta-approximation converges to f in measure as delta goes to zero?

Published on 25 Mar 2026 - 6:06

score 61 · Answer 4 · 2026-03-25 06:06:33

61

Views

Show that $\mu_n=\frac1n\sum_1^n\epsilon(j)$ has infinitely many weak$^*$ limit point

Published on 25 Mar 2026 - 6:06

score 264 · Answer 5 · 2026-03-25 01:31:11

264

Views

Showing $X$ is a Banach space using a sequence of elements $\{x_n\}$ that satisfies two conditions?

Published on 25 Mar 2026 - 1:31

score 163 · Answer 6 · 2018-03-23 15:14:31

163

Views

Given a (separable) Banach space $(X,||.||)$, is there an inner product $<,>$ on $X$ such that $(X,||.||)$ and $(X,<,>)$ are linearly isomorphic?

Published on 23 Mar 2018 - 15:14

score 39 · Answer 7 · 2018-03-24 14:15:18

39

Views

"Basic" question about Banach spaces, projections

Published on 24 Mar 2018 - 14:15

score 1k · Answer 8 · 2026-03-25 12:16:29

1k

Views

$||x||_2\leq ||x||_1\leq \sqrt{n}||x||_2$

Published on 25 Mar 2026 - 12:16

score 269 · Answer 9 · 2026-03-25 14:12:21

269

Views

A problem on application of Hahn-Banach theorem

Published on 25 Mar 2026 - 14:12

score 128 · Answer 10 · 2018-03-26 03:54:13

128

Views

Geometric Interpretation of Kadec-Snobar

Published on 26 Mar 2018 - 3:54

score 1.3k · Answer 11 · 2026-03-25 10:57:29

1.3k

Views

If every subsequence of $(x_n)$ has a subsequence converging weakly to $x$ then $x_n$ converges weakly to $x$.

Published on 25 Mar 2026 - 10:57

score 82 · Answer 12 · 2026-02-23 06:35:00

82

Views

Hahn Banach extension type theorem

Published on 23 Feb 2026 - 6:35

score 19 · Answer 13 · 2026-03-25 01:27:59

19

Views

Let $(N,\|\cdot\|)$ be a normed space. If $\dim{N}<\infty$ then every Cauchy sequence of $N$ converges.

Published on 25 Mar 2026 - 1:27

score 31 · Answer 14 · 2018-03-28 13:53:47

31

Views

show that $f_n \xrightarrow{w^*} 0$ in $l^\infty$.

Published on 28 Mar 2018 - 13:53

score 111 · Answer 15 · 2026-03-24 23:59:17

111

Views

Isomorphic quotient spaces

Published on 24 Mar 2026 - 23:59

List Question

A subspace $Y$ of a Banach space $X$ is complete iff the set $Y$ is closed in $X$.

Non-linear functional on a Banach space

(From Royden 3rd Ed )How to prove the delta-approximation converges to f in measure as delta goes to zero?

Show that $\mu_n=\frac1n\sum_1^n\epsilon(j)$ has infinitely many weak$^*$ limit point

Showing $X$ is a Banach space using a sequence of elements $\{x_n\}$ that satisfies two conditions?

Given a (separable) Banach space $(X,||.||)$, is there an inner product $<,>$ on $X$ such that $(X,||.||)$ and $(X,<,>)$ are linearly isomorphic?

"Basic" question about Banach spaces, projections

$||x||_2\leq ||x||_1\leq \sqrt{n}||x||_2$

A problem on application of Hahn-Banach theorem

Geometric Interpretation of Kadec-Snobar

If every subsequence of $(x_n)$ has a subsequence converging weakly to $x$ then $x_n$ converges weakly to $x$.

Hahn Banach extension type theorem

Let $(N,\|\cdot\|)$ be a normed space. If $\dim{N}<\infty$ then every Cauchy sequence of $N$ converges.

show that $f_n \xrightarrow{w^*} 0$ in $l^\infty$.

Isomorphic quotient spaces

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