Question

Is there any guarantee that a norm one operator, $T$ will attain its norm at some extreme point?

score 90 · Answer 1 · 2023-08-03 06:19:13

90

Views

Is there any guarantee that a norm one operator, $T$ will attain its norm at some extreme point?

Published on 03 Aug 2023 - 6:19

score 33 · Answer 2 · 2026-03-28 11:35:29

33

Views

Brezis' exercise 6.25(i): the existence of $M,P \in \mathcal L(E)$ such that $M \circ(I+K)=I-P$

Published on 28 Mar 2026 - 11:35

score 31 · Answer 3 · 2026-03-28 11:34:08

31

Views

Brezis' exercise 6.25(ii): the existence of $\widetilde M, \widetilde P \in \mathcal L(E)$ such that $(I+K) \circ \widetilde M = I-\widetilde P$

Published on 28 Mar 2026 - 11:34

score 45 · Answer 4 · 2023-08-04 01:45:21

45

Views

Confused about a part of the proof for $\mathcal{L}(V, W)$ is Banach provided that $V$ is normed and $W$ is Banach.

Published on 04 Aug 2023 - 1:45

score 73 · Answer 5 · 2026-03-28 08:50:11

73

Views

If all unital Banach algebras contain maximal ideals, then why doesn't $M_n(\mathbb{C})$ have proper ideals?

Published on 28 Mar 2026 - 8:50

score 107 · Answer 6 · 2026-03-28 06:16:36

107

Views

Question on a proof that a space of linear map between normed spaces is a Banach space when the arrival space is a Banach space

Published on 28 Mar 2026 - 6:16

score 86 · Answer 7 · 2023-08-06 02:42:31

86

Views

Does $ W_1\hookrightarrow W_2 \hookrightarrow\hookrightarrow W_3$ imply that $W_1 \hookrightarrow\hookrightarrow W_3$?

Published on 06 Aug 2023 - 2:42

score 35 · Answer 8 · 2023-08-07 20:05:54

35

Views

Relation between space of bounded holomorphic mappings and space of little Bloch mappings

Published on 07 Aug 2023 - 20:05

score 60 · Answer 9 · 2026-04-06 11:13:51

60

Views

Convergence in $L^p$ preserves density

Published on 06 Apr 2026 - 11:13

score 35 · Answer 10 · 2023-08-08 17:13:54

35

Views

Intuition: Inclusion of balls leads to reverse inclusion of norm, even upon rescaling?

Published on 08 Aug 2023 - 17:13

score 45 · Answer 11 · 2023-08-09 13:28:47

45

Views

Is there non-zero vector with bounded orbit if the set of vectors with unbounded is residual and open in Banach space $X$?

Published on 09 Aug 2023 - 13:28

score 128 · Answer 12 · 2026-03-25 19:00:37

128

Views

Mathematical Method of Geometric Second Quantization?

Published on 25 Mar 2026 - 19:00

score 196 · Answer 13 · 2023-08-11 10:00:28

196

Views

Banach space which has Radon-Nikodym Property +Weakly sequentially complete but not reflexive.

Published on 11 Aug 2023 - 10:00

score 68 · Answer 14 · 2026-03-29 11:08:36

68

Views

Closure of balanced convex set and its dilation

Published on 29 Mar 2026 - 11:08

score 83 · Answer 15 · 2023-08-13 17:33:58

83

Views

What topology is given to $L(X,Y)$?

Published on 13 Aug 2023 - 17:33

List Question

Is there any guarantee that a norm one operator, $T$ will attain its norm at some extreme point?

Brezis' exercise 6.25(i): the existence of $M,P \in \mathcal L(E)$ such that $M \circ(I+K)=I-P$

Brezis' exercise 6.25(ii): the existence of $\widetilde M, \widetilde P \in \mathcal L(E)$ such that $(I+K) \circ \widetilde M = I-\widetilde P$

Confused about a part of the proof for $\mathcal{L}(V, W)$ is Banach provided that $V$ is normed and $W$ is Banach.

If all unital Banach algebras contain maximal ideals, then why doesn't $M_n(\mathbb{C})$ have proper ideals?

Question on a proof that a space of linear map between normed spaces is a Banach space when the arrival space is a Banach space

Does $ W_1\hookrightarrow W_2 \hookrightarrow\hookrightarrow W_3$ imply that $W_1 \hookrightarrow\hookrightarrow W_3$?

Relation between space of bounded holomorphic mappings and space of little Bloch mappings

Convergence in $L^p$ preserves density

Intuition: Inclusion of balls leads to reverse inclusion of norm, even upon rescaling?

Is there non-zero vector with bounded orbit if the set of vectors with unbounded is residual and open in Banach space $X$?

Mathematical Method of Geometric Second Quantization?

Banach space which has Radon-Nikodym Property +Weakly sequentially complete but not reflexive.

Closure of balanced convex set and its dilation

What topology is given to $L(X,Y)$?

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