List questions from banach-spaces

Published on 14 Apr 2026 - 5:21

603

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Compact subsets of function spaces, geometry

Published on 12 Apr 2026 - 7:09

1.3k

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How to prove that sequence spaces $l^{p}, l^{\infty}$ and function space $C[a. b]$ are of infinite dimension

Published on 16 Apr 2026 - 6:49

210

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Geometry of the space $C[a, b]$ respect to the norm $\lVert x \rVert_{\infty} = \max_{t\in [a,b]}\lvert x(t)\rvert$.

Published on 15 Apr 2026 - 21:23

2.4k

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Can we visualize the closed balls for the space $l^{\infty}$ equipped with the $\sup$ norm

Published on 14 Apr 2026 - 9:36

16.4k

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$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$

Published on 15 Apr 2026 - 20:22

868

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$C^{1}[a,b]$ equipped with the norm given by $\lVert x\rVert _{\infty} = \sup_{t\in [0, 1]} \lvert x(t) \rvert$ is an incomplete normed space.

Published on 16 Apr 2026 - 10:01

194

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An orbit of a group action and the implicit function theorem

Published on 11 Apr 2026 - 3:06

260

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Is the adjoint operation WOT-WOT continuous?

Published on 08 Apr 2026 - 16:05

78

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Banach Space Condition help

Published on 14 Apr 2026 - 18:51

131

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$\lVert A\lVert<1$ implies $1-A$ invertible only true in complete spaces?

Published on 14 Apr 2026 - 20:41

1.7k

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Proof of the Riesz Representation Theorem

Published on 26 Mar 2026 - 11:06

180

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$\mathbb N$ a Banach space?

Published on 15 Apr 2026 - 16:57

1.3k

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If $X^\ast $ is separable $\Longrightarrow$ $S_{X^\ast}$ is also separable

Published on 14 Apr 2026 - 9:18

698

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Continuity of bilinear form

Published on 11 Apr 2026 - 17:09

List Question

Banach subsequence converges

Compact subsets of function spaces, geometry

How to prove that sequence spaces $l^{p}, l^{\infty}$ and function space $C[a. b]$ are of infinite dimension

Geometry of the space $C[a, b]$ respect to the norm $\lVert x \rVert_{\infty} = \max_{t\in [a,b]}\lvert x(t)\rvert$.

Can we visualize the closed balls for the space $l^{\infty}$ equipped with the $\sup$ norm

$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$

$C^{1}[a,b]$ equipped with the norm given by $\lVert x\rVert _{\infty} = \sup_{t\in [0, 1]} \lvert x(t) \rvert$ is an incomplete normed space.

An orbit of a group action and the implicit function theorem

Is the adjoint operation WOT-WOT continuous?

Banach Space Condition help

$\lVert A\lVert<1$ implies $1-A$ invertible only true in complete spaces?

Proof of the Riesz Representation Theorem

$\mathbb N$ a Banach space?

If $X^\ast $ is separable $\Longrightarrow$ $S_{X^\ast}$ is also separable

Continuity of bilinear form

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