List questions from banach-spaces

Published on 02 Apr 2026 - 10:37

663

Views

Some subspaces of $l^1$ are closed

Published on 29 Mar 2026 - 14:18

32

Views

Bounding an Unbounded operator and preserving Kernel

Published on 28 Mar 2026 - 16:19

370

Views

In what sense is $S^\infty$ the same as $\{x \in \ell_2 : \|x\| = 1 \}$?

Published on 17 Oct 2016 - 17:00

495

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Infinite matrix operator

Published on 17 Oct 2016 - 23:24

261

Views

Question about unconditional Schauder basis definition

Published on 25 Mar 2026 - 6:31

80

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Boundedness of sequence $ \{||T_n || \} $ in Banach space.

Published on 18 Oct 2016 - 13:03

711

Views

Failure of closed graph theorem in this example

Published on 26 Mar 2026 - 1:00

375

Views

Closed convex hull of a weakly convergent sequence has empty interior in an infinite-dimensional Banach space

Published on 25 Mar 2026 - 22:04

56

Views

Proof that $ \|x+y\|^2 + c^2\|x-y\|^2 \leq 2\|x\|^2 + 2\|y\|^2, \forall x,y \in V$.

Published on 19 Oct 2016 - 12:38

115

Views

Understanding the proof that $C_b(\mathbb{R})$ is complete.

Published on 19 Oct 2016 - 13:08

70

Views

Limit of a sequence of functionals $F_n : C([0,1]) \to \mathbb{R}$

Published on 19 Oct 2016 - 13:13

40

Views

Existence of bounded continuous $f:\mathbb{R} \to \mathbb{R}$ st. $\sup_{n \in \mathbb{N}}| \int_{-n}^{n} f(t)\sin(2 \pi n t)dt| = \infty$

Published on 19 Oct 2016 - 14:21

126

Views

Complete domain is necessary for Banach-Steinhaus Theorem

Published on 19 Oct 2016 - 17:12

48

Views

A series of sequences in $l^{p}$ is a linear continuous functional

Published on 19 Oct 2016 - 17:34

List Question

Eigenvalues of bounded linear operator

Some subspaces of $l^1$ are closed

Bounding an Unbounded operator and preserving Kernel

In what sense is $S^\infty$ the same as $\{x \in \ell_2 : \|x\| = 1 \}$?

Infinite matrix operator

Question about unconditional Schauder basis definition

Boundedness of sequence $ \{||T_n || \} $ in Banach space.

Failure of closed graph theorem in this example

Closed convex hull of a weakly convergent sequence has empty interior in an infinite-dimensional Banach space

Proof that $ \|x+y\|^2 + c^2\|x-y\|^2 \leq 2\|x\|^2 + 2\|y\|^2, \forall x,y \in V$.

Understanding the proof that $C_b(\mathbb{R})$ is complete.

Limit of a sequence of functionals $F_n : C([0,1]) \to \mathbb{R}$

Existence of bounded continuous $f:\mathbb{R} \to \mathbb{R}$ st. $\sup_{n \in \mathbb{N}}| \int_{-n}^{n} f(t)\sin(2 \pi n t)dt| = \infty$

Complete domain is necessary for Banach-Steinhaus Theorem

A series of sequences in $l^{p}$ is a linear continuous functional

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