Question

Banach space is direct sum of closed subspaces. Do these subspaces become continuous embeddings?

score 76 · Answer 1 · 2017-03-19 02:37:08

Banach space is direct sum of closed subspaces. Do these subspaces become continuous embeddings?

Published on 19 Mar 2017 - 2:37

score 152 · Answer 2 · 2017-03-19 09:01:58

If the sum of elements of a Banach space indexed by an arbitrary set converges then at most countably many of the elements in the sum is non-zero?

score 1.9k · Answer 3 · 2017-03-19 22:02:41

1.9k

Views

Bilinear map of Banach spaces separately continuous implies continuous: Use of uniform boundedness principle

Published on 19 Mar 2017 - 22:02

score 514 · Answer 4 · 2026-03-26 02:46:48

514

Views

Intuitive meaning of high order Fréchet derivative $D^k f_p(v_1, \cdots, v_l)$

Published on 26 Mar 2026 - 2:46

score 1.1k · Answer 5 · 2026-03-29 12:12:04

1.1k

Views

Prove that in a Banach space every nonempty open set is of the second category

Published on 29 Mar 2026 - 12:12

score 93 · Answer 6 · 2017-03-21 12:11:30

93

Views

Show that $\mathcal l^{\infty}$ with norm $\Vert x\Vert = \sup_{k\in \mathbb N}|x_k|$ is Banach space

Published on 21 Mar 2017 - 12:11

score 1.3k · Answer 7 · 2017-03-21 14:46:03

1.3k

Views

Strict minimizer versus strong minimizer

Published on 21 Mar 2017 - 14:46

score 57 · Answer 8 · 2017-03-21 20:08:15

57

Views

A convergent sequence in $\ell_1$ that is $1/2$-distant to the standard basis

Published on 21 Mar 2017 - 20:08

score 38 · Answer 9 · 2026-03-25 08:05:35

38

Views

Why this set is countable?

Published on 25 Mar 2026 - 8:05

score 478 · Answer 10 · 2017-03-22 01:19:00

478

Views

Convex Hull of a balanced set is balanced

Published on 22 Mar 2017 - 1:19

score 487 · Answer 11 · 2017-03-22 05:53:58

487

Views

How to show that the projections onto the summands in a direct sum decomposition of a Banach space have the same Lipchitz constant?

Published on 22 Mar 2017 - 5:53

score 73 · Answer 12 · 2017-03-22 06:04:48

73

Views

How do I show the following result for two commuting bounded idempotent linear operators on a normed space?

Published on 22 Mar 2017 - 6:04

score 525 · Answer 13 · 2017-03-22 07:31:37

525

Views

Each normed space is isometrically isomorphic to a dense subset of a Banach space

Published on 22 Mar 2017 - 7:31

score 475 · Answer 14 · 2017-03-23 13:03:30

475

Views

$\ell_{\infty}$ and the bounded approximation property

Published on 23 Mar 2017 - 13:03

score 298 · Answer 15 · 2017-03-25 12:55:40

298

Views

Gaussian measure on sequence space

Published on 25 Mar 2017 - 12:55

List Question

Banach space is direct sum of closed subspaces. Do these subspaces become continuous embeddings?

If the sum of elements of a Banach space indexed by an arbitrary set converges then at most countably many of the elements in the sum is non-zero?

Bilinear map of Banach spaces separately continuous implies continuous: Use of uniform boundedness principle

Intuitive meaning of high order Fréchet derivative $D^k f_p(v_1, \cdots, v_l)$

Prove that in a Banach space every nonempty open set is of the second category

Show that $\mathcal l^{\infty}$ with norm $\Vert x\Vert = \sup_{k\in \mathbb N}|x_k|$ is Banach space

Strict minimizer versus strong minimizer

A convergent sequence in $\ell_1$ that is $1/2$-distant to the standard basis

Why this set is countable?

Convex Hull of a balanced set is balanced

How to show that the projections onto the summands in a direct sum decomposition of a Banach space have the same Lipchitz constant?

How do I show the following result for two commuting bounded idempotent linear operators on a normed space?

Each normed space is isometrically isomorphic to a dense subset of a Banach space

$\ell_{\infty}$ and the bounded approximation property

Gaussian measure on sequence space

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