List questions from banach-spaces

Published on 01 Nov 2019 - 16:01

48

Views

Application of Yosida Theorem

Published on 27 Mar 2026 - 13:45

166

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Prove that $T$ is continuous.

Published on 02 Nov 2019 - 14:05

189

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Prove that the derivative (if exists) is unique

Published on 02 Nov 2019 - 16:11

61

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Why does the author said "When $\mathcal{L}(E, F)$ is a Banach space, we can meaningfully speak of the continuity of the derivative"?

Published on 02 Nov 2019 - 16:37

40

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How to reconcile the formulas of chain rule in cases $X \subseteq \mathbb K$ and $X$ is a general Banach space?

Published on 29 Mar 2026 - 11:50

264

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Compactness of open map

Published on 27 Mar 2026 - 7:57

57

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Prove that $L(l, Y) $ and $l_y^\infty $are isometrically isomorphic spaces.

Published on 25 Mar 2026 - 14:47

22

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Formula for $E[X|\mathcal{A}]$, $\mathcal{A}=\sigma(\{[0,\frac12]\})$, $X\in L^2$

Published on 01 Apr 2026 - 7:22

50

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About the completeness of a normed space

Published on 28 Mar 2026 - 4:34

76

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Help with a theorem of H. Rosenthal

Published on 08 Nov 2019 - 1:07

69

Views

$\mathbb{R^n}$ with a norm $||.||$, where $(\mathbb{R^n},||.||)$ is a Banach space

Published on 25 Mar 2026 - 12:53

281

Views

Let $(a_n)\subset\mathbb{C}$ be bounded. Then $T_a\colon\ell^p\to\ell^p, \ (T_a x)_n:=a_n x_n$ compact iff $a_n\to0$.

Published on 26 Mar 2026 - 19:02

26

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Relation between uniform convergence and continuity question

Published on 09 Nov 2019 - 15:51

33

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Comparision of a theorem in Banach Space with Hilbert Space

Published on 10 Nov 2019 - 1:34

List Question

pullback of closure of closed subspace under a Banach space embedding

Application of Yosida Theorem

Prove that $T$ is continuous.

Prove that the derivative (if exists) is unique

Why does the author said "When $\mathcal{L}(E, F)$ is a Banach space, we can meaningfully speak of the continuity of the derivative"?

How to reconcile the formulas of chain rule in cases $X \subseteq \mathbb K$ and $X$ is a general Banach space?

Compactness of open map

Prove that $L(l, Y) $ and $l_y^\infty $are isometrically isomorphic spaces.

Formula for $E[X|\mathcal{A}]$, $\mathcal{A}=\sigma(\{[0,\frac12]\})$, $X\in L^2$

About the completeness of a normed space

Help with a theorem of H. Rosenthal

$\mathbb{R^n}$ with a norm $||.||$, where $(\mathbb{R^n},||.||)$ is a Banach space

Let $(a_n)\subset\mathbb{C}$ be bounded. Then $T_a\colon\ell^p\to\ell^p, \ (T_a x)_n:=a_n x_n$ compact iff $a_n\to0$.

Relation between uniform convergence and continuity question

Comparision of a theorem in Banach Space with Hilbert Space

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