Question

Problem 1.70 of Megginson's "An Introduction to Banach Space Theory"

score 193 · Answer 1 · 2026-03-25 05:45:53

193

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Problem 1.70 of Megginson's "An Introduction to Banach Space Theory"

Published on 25 Mar 2026 - 5:45

score 3.9k · Answer 2 · 2026-03-23 19:18:49

3.9k

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Is the cartesian product of two Hilbert spaces a Hilbert space?

Published on 23 Mar 2026 - 19:18

score 330 · Answer 3 · 2026-03-20 16:43:49

330

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Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?

Published on 20 Mar 2026 - 16:43

score 61 · Answer 4 · 2026-03-22 06:36:12

61

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Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?

Published on 22 Mar 2026 - 6:36

score 324 · Answer 5 · 2026-03-20 08:54:03

324

Views

Identify $\operatorname{co}(\{e_n:n\in\mathbb N\})$ and $\overline{\operatorname{co}}(\{e_n : n\in\mathbb N\})$ in $c_0$ and $\ell^p$

Published on 20 Mar 2026 - 8:54

score 182 · Answer 6 · 2026-03-21 06:17:00

182

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Theorem 1.7.9 of Megginson: Completeness is a three-space property.

Published on 21 Mar 2026 - 6:17

score 85 · Answer 7 · 2026-03-22 12:29:59

85

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A weakly open subset of the unit ball of the Read's space $R$ (an infinite-dimensional Banach space) is unbounded.

Published on 22 Mar 2026 - 12:29

score 241 · Answer 8 · 2026-03-20 07:23:43

241

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Separability of differentiable functions

Published on 20 Mar 2026 - 7:23

score 77 · Answer 9 · 2026-03-22 18:49:09

Showing $u_{\lambda}(x):= \left(\frac{\lambda}{{\lambda}^{2}+|x|^2}\right)^{\frac{n-2}{2}}$ is not sequentially compact in $L^{2^{*}}$

score 164 · Answer 10 · 2026-03-18 07:38:37

164

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Proving that a composition of bounded operator and trace class operator is trace class

Published on 18 Mar 2026 - 7:38

score 561 · Answer 11 · 2026-03-19 16:04:55

561

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Weak convergence in a reﬂexive, separable and infinite Banach space.

Published on 19 Mar 2026 - 16:04

score 85 · Answer 12 · 2026-03-25 03:03:10

85

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Values of $\alpha$ such that the inverse of a linear operator is bounded

Published on 25 Mar 2026 - 3:03

score 57 · Answer 13 · 2026-03-25 03:03:18

57

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The name and properties of the convergence of measures in the weak topology

Published on 25 Mar 2026 - 3:03

score 50 · Answer 14 · 2026-03-24 23:49:54

50

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If $V$ is a subspace of $\ell^2$ that doesn't contain a sequence which has only finitely many nonzero elements, can the closure of $V$ contain it?

Published on 24 Mar 2026 - 23:49

score 117 · Answer 15 · 2026-03-19 23:42:37

117

Views

orthogonal complement - incorrect Brézis definition

Published on 19 Mar 2026 - 23:42

List Question

Problem 1.70 of Megginson's "An Introduction to Banach Space Theory"

Is the cartesian product of two Hilbert spaces a Hilbert space?

Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?

Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?

Identify $\operatorname{co}(\{e_n:n\in\mathbb N\})$ and $\overline{\operatorname{co}}(\{e_n : n\in\mathbb N\})$ in $c_0$ and $\ell^p$

Theorem 1.7.9 of Megginson: Completeness is a three-space property.

A weakly open subset of the unit ball of the Read's space $R$ (an infinite-dimensional Banach space) is unbounded.

Separability of differentiable functions

Showing $u_{\lambda}(x):= \left(\frac{\lambda}{{\lambda}^{2}+|x|^2}\right)^{\frac{n-2}{2}}$ is not sequentially compact in $L^{2^{*}}$

Proving that a composition of bounded operator and trace class operator is trace class

Weak convergence in a reﬂexive, separable and infinite Banach space.

Values of $\alpha$ such that the inverse of a linear operator is bounded

The name and properties of the convergence of measures in the weak topology

If $V$ is a subspace of $\ell^2$ that doesn't contain a sequence which has only finitely many nonzero elements, can the closure of $V$ contain it?

orthogonal complement - incorrect Brézis definition

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