List questions from banach-spaces

Published on 08 Dec 2019 - 22:53

148

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Weighted Lebesgue spaces

Published on 11 Dec 2019 - 6:03

36

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$|\phi'(x)<1|$ is sufficient to show that $\phi$ is a contraction, so is $\phi'(x)>1$ sufficient to show $\phi$ isn't a contraction?

Published on 25 Mar 2026 - 22:30

73

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Continuity of the distance from one dimensional subspaces in Banach spaces

Published on 26 Mar 2026 - 22:57

1.4k

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Showing that space of absolutely continuous functions is Banach space

Published on 23 Feb 2026 - 8:32

190

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Proof of the equivalence of the norms in Banach spaces (infinite dimension)

Published on 12 Dec 2019 - 17:10

1.4k

Views

If a linear operator $A$ is closed and injective, then its inverse $A^{-1}$ is also closed

Published on 12 Dec 2019 - 19:08

819

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$T:X \to Y$ linear, $J:Y \to Z$ linear, injective and bounded such that $JT:X\to Z$ is bounded, too. Prove $T$ is bounded.

Published on 12 Dec 2019 - 21:59

420

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Let $(C[-1,1],\|.\|_2)$ prove this space isn't a Banach space.

Published on 13 Dec 2019 - 16:02

45

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Is the point-oscillation of a (discontinuous) linear functional continuous?

Published on 14 Dec 2019 - 9:12

48

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Permute transposition and derivative + Norm question

Published on 14 Dec 2019 - 11:52

931

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Are Banach norms Fréchet differentiable?

Published on 25 Mar 2026 - 18:24

269

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Are strictly convex Banach norms Fréchet differentiable?

Published on 25 Mar 2026 - 18:31

66

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Are all FD-spaces strictly convex?

Published on 25 Mar 2026 - 18:24

248

Views

Derivative of Inverse Function on Banach Space

Published on 19 Dec 2019 - 3:50

List Question

Closed Graph Theorem in Royden-Fitzpatrick

Weighted Lebesgue spaces

$|\phi'(x)<1|$ is sufficient to show that $\phi$ is a contraction, so is $\phi'(x)>1$ sufficient to show $\phi$ isn't a contraction?

Continuity of the distance from one dimensional subspaces in Banach spaces

Showing that space of absolutely continuous functions is Banach space

Proof of the equivalence of the norms in Banach spaces (infinite dimension)

If a linear operator $A$ is closed and injective, then its inverse $A^{-1}$ is also closed

$T:X \to Y$ linear, $J:Y \to Z$ linear, injective and bounded such that $JT:X\to Z$ is bounded, too. Prove $T$ is bounded.

Let $(C[-1,1],\|.\|_2)$ prove this space isn't a Banach space.

Is the point-oscillation of a (discontinuous) linear functional continuous?

Permute transposition and derivative + Norm question

Are Banach norms Fréchet differentiable?

Are strictly convex Banach norms Fréchet differentiable?

Are all FD-spaces strictly convex?

Derivative of Inverse Function on Banach Space

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