List questions from banach-spaces

Published on 02 Mar 2018 - 3:47

46

Views

New norms on $L^2$

Published on 25 Mar 2026 - 3:07

462

Views

Linear map between $L^p$ and $L^q$.

Published on 25 Mar 2026 - 2:59

1.7k

Views

Intuition behind Lebesgue spaces: Lp, L^p, $\mathcal L^p$ or $L^p$ / $\ell^p$?

Published on 25 Mar 2026 - 3:03

92

Views

A corollary of Hahn-Banach

Published on 04 Mar 2018 - 21:32

31

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How to prove that a sequence $f_{n} \in L^{1}$?

Published on 22 Mar 2026 - 13:55

114

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Non-Reflexivity of $L^1$ by finding a particular operator in the dual space?

Published on 22 Mar 2026 - 16:45

108

Views

When does order convergence imply topological convergence?

Published on 17 Mar 2026 - 15:59

83

Views

Second dual of the image of a Banach space under a continuous linear operator

Published on 24 Mar 2026 - 22:17

253

Views

Finding a maximal orthonormal set in a Hilbert space

Published on 25 Mar 2026 - 9:35

35

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Show that $\forall \phi\in X^*,\,|\phi(x_n)|\le M_1,\,\forall n\in\mathbb N\implies |x_n|\le M_2,\,\forall n\in\mathbb N$

Published on 07 Mar 2018 - 15:09

4.5k

Views

What does it mean for an operator to be diagonal with respect to an orthonormal basis?

Published on 08 Mar 2018 - 11:36

189

Views

The algebra of diagonal operators on a Hilbert space is a Banach algebra

Published on 25 Mar 2026 - 9:28

37

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If $ \|G(x+ty)\|<\|G(x)\| $, is then $ \|G(x) + tG'(x)[y]\| <\|G(x)\| $?

Published on 22 Mar 2026 - 10:14

259

Views

Fixed point theorems, convexity, contractibility

Published on 25 Mar 2026 - 2:59

List Question

The convex hull of a precompact set in a Banach space is precompact

New norms on $L^2$

Linear map between $L^p$ and $L^q$.

Intuition behind Lebesgue spaces: Lp, L^p, $\mathcal L^p$ or $L^p$ / $\ell^p$?

A corollary of Hahn-Banach

How to prove that a sequence $f_{n} \in L^{1}$?

Non-Reflexivity of $L^1$ by finding a particular operator in the dual space?

When does order convergence imply topological convergence?

Second dual of the image of a Banach space under a continuous linear operator

Finding a maximal orthonormal set in a Hilbert space

Show that $\forall \phi\in X^*,\,|\phi(x_n)|\le M_1,\,\forall n\in\mathbb N\implies |x_n|\le M_2,\,\forall n\in\mathbb N$

What does it mean for an operator to be diagonal with respect to an orthonormal basis?

The algebra of diagonal operators on a Hilbert space is a Banach algebra

If $ \|G(x+ty)\|<\|G(x)\| $, is then $ \|G(x) + tG'(x)[y]\| <\|G(x)\| $?

Fixed point theorems, convexity, contractibility

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