List questions from banach-spaces

Published on 15 Feb 2019 - 18:11

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Normed space $C^2[0,1]$ with norm $\lVert f\rVert:=\max_{t\in[0,1]}\{\lvert f(t)\rvert+\lvert f''(t)\rvert\}$ is Banach space

Published on 25 Mar 2026 - 22:26

91

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Tensor product of function spaces: does $\widehat{\bigotimes}_{\pi;1\leq k\leq n}C(X_{k})^{\prime}\cong C(\prod_{k}X)^{\prime}$ hold?

Published on 17 Feb 2019 - 20:07

235

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Show that the following is bounded and surjective (Folland exercise 5.36)

Published on 17 Feb 2019 - 21:22

106

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Every bounded net in a dual space has a cluster point?

Published on 25 Mar 2026 - 12:49

101

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$L^2$ and $C^0$ norms combined

Published on 19 Feb 2019 - 19:46

178

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Annihilator norm has a minimizer?

Published on 20 Feb 2019 - 19:22

47

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Is this subspace isomorphic to $\ell^1$?

Published on 21 Feb 2019 - 12:15

90

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On a sequence $f_k$ in $L^{2+\frac{1}{k}}$

Published on 23 Feb 2026 - 12:34

124

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Question about weak convergence in Banach space

Published on 22 Feb 2019 - 12:07

24

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Contraction function.

Published on 22 Feb 2019 - 14:22

78

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If $\|A(x)\|_Y \geq c \|x\|_X$ and $\dim X = + \infty$, can $A \in \mathcal{L}(X,Y)$ be a compact operator?

Published on 25 Mar 2026 - 23:38

30

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Showing that $0 \in \overline{A(\partial B_1^X)}$ if $X,Y$ Banach with $\dim X = + \infty$ and $A \in \mathcal{L}_c(X,Y)$.

Published on 25 Mar 2026 - 17:42

50

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Differentiability of partial function function

Published on 25 Mar 2026 - 13:23

29

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Question about notation in Banach spaces problem

Published on 23 Feb 2026 - 1:01

List Question

Showing weakly continuous operators are continuous without using weak topology

Normed space $C^2[0,1]$ with norm $\lVert f\rVert:=\max_{t\in[0,1]}\{\lvert f(t)\rvert+\lvert f''(t)\rvert\}$ is Banach space

Tensor product of function spaces: does $\widehat{\bigotimes}_{\pi;1\leq k\leq n}C(X_{k})^{\prime}\cong C(\prod_{k}X)^{\prime}$ hold?

Show that the following is bounded and surjective (Folland exercise 5.36)

Every bounded net in a dual space has a cluster point?

$L^2$ and $C^0$ norms combined

Annihilator norm has a minimizer?

Is this subspace isomorphic to $\ell^1$?

On a sequence $f_k$ in $L^{2+\frac{1}{k}}$

Question about weak convergence in Banach space

Contraction function.

If $\|A(x)\|_Y \geq c \|x\|_X$ and $\dim X = + \infty$, can $A \in \mathcal{L}(X,Y)$ be a compact operator?

Showing that $0 \in \overline{A(\partial B_1^X)}$ if $X,Y$ Banach with $\dim X = + \infty$ and $A \in \mathcal{L}_c(X,Y)$.

Differentiability of partial function function

Question about notation in Banach spaces problem

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