Question

Dual of a Banach space

score 34 · Answer 1 · 2026-03-27 19:32:36

34

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Dual of a Banach space

Published on 27 Mar 2026 - 19:32

score 33 · Answer 2 · 2026-03-27 23:14:27

33

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Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Published on 27 Mar 2026 - 23:14

score 76 · Answer 3 · 2026-04-01 21:34:04

76

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Let $L$ be a (topological) complement of $G$. Is $\dim G = \operatorname{codim} L$?

Published on 01 Apr 2026 - 21:34

score 153 · Answer 4 · 2023-05-20 15:30:05

153

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If $G$ has finite codimension, then $G$ has a complement

Published on 20 May 2023 - 15:30

score 51 · Answer 5 · 2023-05-20 21:22:17

51

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Let $N$ be a $p$-dimensional subspace of $E^*$ and $G := N^\perp$. Then $\operatorname{codim} G = p$

Published on 20 May 2023 - 21:22

score 50 · Answer 6 · 2023-05-21 09:13:41

50

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How a contradiction is obtained in a proof of the Fredholm alternative?

Published on 21 May 2023 - 9:13

score 55 · Answer 7 · 2026-03-27 23:13:48

55

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About the injectivity and surjectivity of the map $T = (\lambda I - K)|_{\mathfrak{R}}$

Published on 27 Mar 2026 - 23:13

score 76 · Answer 8 · 2026-03-27 13:25:39

76

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Prove that the Faber-Schauder System is a basis for $C[0,1]$ with the sup norm.

Published on 27 Mar 2026 - 13:25

score 77 · Answer 9 · 2026-03-26 01:34:54

77

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Proving that a sequence $\{\delta_n\} \in \ell_\infty^$ has no weak- convergent subsequence but has a weak-* convergent subnet

Published on 26 Mar 2026 - 1:34

score 53 · Answer 10 · 2026-03-25 08:07:03

53

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Are spreading sequences uniformly spreading?

Published on 25 Mar 2026 - 8:07

score 49 · Answer 11 · 2023-05-25 13:17:52

49

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Question on the definition of a norm of a linear transformation

Published on 25 May 2023 - 13:17

score 43 · Answer 12 · 2023-05-25 22:31:45

43

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Does a statement similar to Riesz's lemma hold?

Published on 25 May 2023 - 22:31

score 132 · Answer 13 · 2026-03-27 17:52:57

132

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If $L_n \rightarrow L \in X^$ in the weak sense and $x_n \rightarrow x$ in norm, does $L_n(x_n) \rightarrow L(x)$?

Published on 27 Mar 2026 - 17:52

score 75 · Answer 14 · 2023-05-26 08:32:16

75

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Lemma 6.2. in Brezis' Functional Analysis

Published on 26 May 2023 - 8:32

score 96 · Answer 15 · 2023-05-26 09:29:43

96

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Is there a bounded sequence $(e_n)$ such that $e_n \in E_n$ and that $(e_n)$ does not have any convergent subsequence?

Published on 26 May 2023 - 9:29

List Question

Dual of a Banach space

Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Let $L$ be a (topological) complement of $G$. Is $\dim G = \operatorname{codim} L$?

If $G$ has finite codimension, then $G$ has a complement

Let $N$ be a $p$-dimensional subspace of $E^*$ and $G := N^\perp$. Then $\operatorname{codim} G = p$

How a contradiction is obtained in a proof of the Fredholm alternative?

About the injectivity and surjectivity of the map $T = (\lambda I - K)|_{\mathfrak{R}}$

Prove that the Faber-Schauder System is a basis for $C[0,1]$ with the sup norm.

Proving that a sequence $\{\delta_n\} \in \ell_\infty^$ has no weak- convergent subsequence but has a weak-* convergent subnet

Are spreading sequences uniformly spreading?

Question on the definition of a norm of a linear transformation

Does a statement similar to Riesz's lemma hold?

If $L_n \rightarrow L \in X^$ in the weak sense and $x_n \rightarrow x$ in norm, does $L_n(x_n) \rightarrow L(x)$?

Lemma 6.2. in Brezis' Functional Analysis

Is there a bounded sequence $(e_n)$ such that $e_n \in E_n$ and that $(e_n)$ does not have any convergent subsequence?

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