Question

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

score 3.9k · Answer 1 · 2026-05-10 19:17:34

3.9k

Views

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

Published on 10 May 2026 - 19:17

score 111 · Answer 2 · 2026-04-12 07:30:06

111

Views

Non-linear functional on a Banach space

Published on 12 Apr 2026 - 7:30

score 56 · Answer 3 · 2026-05-10 17:39:37

56

Views

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

Published on 10 May 2026 - 17:39

score 64 · Answer 4 · 2026-05-10 17:39:01

64

Views

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

Published on 10 May 2026 - 17:39

score 267 · Answer 5 · 2026-05-10 15:09:37

267

Views

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

Published on 10 May 2026 - 15:09

score 166 · Answer 6 · 2026-04-16 00:52:11

166

Views

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

Published on 16 Apr 2026 - 0:52

score 42 · Answer 7 · 2026-04-11 17:44:38

42

Views

"Basic" question about Banach spaces, projections

Published on 11 Apr 2026 - 17:44

score 1k · Answer 8 · 2026-05-10 16:04:56

1k

Views

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

Published on 10 May 2026 - 16:04

score 272 · Answer 9 · 2026-05-10 12:32:45

272

Views

A problem on application of Hahn-Banach theorem

Published on 10 May 2026 - 12:32

score 131 · Answer 10 · 2026-04-14 08:14:14

131

Views

Geometric Interpretation of Kadec-Snobar

Published on 14 Apr 2026 - 8:14

score 1.3k · Answer 11 · 2026-05-10 15:10:00

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 10 May 2026 - 15:10

score 84 · Answer 12 · 2026-04-09 13:04:31

84

Views

Hahn Banach extension type theorem

Published on 09 Apr 2026 - 13:04

score 22 · Answer 13 · 2026-05-10 15:09:57

22

Views

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

Published on 10 May 2026 - 15:09

score 34 · Answer 14 · 2026-04-17 09:59:17

34

Views

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

Published on 17 Apr 2026 - 9:59

score 113 · Answer 15 · 2026-05-10 15:49:39

113

Views

Isomorphic quotient spaces

Published on 10 May 2026 - 15:49

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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