List questions from banach-spaces

Published on 24 Jan 2017 - 23:00

248

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Prove a differentiable function between banach spaces is continuous

Published on 27 Jan 2017 - 15:42

3.1k

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Prove $C^1([0,1]) $ is Banach.

Published on 28 Jan 2017 - 14:19

361

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from weakly convergent sequence to strongly convergent sequence in a non-compact operator

Published on 29 Jan 2017 - 11:32

263

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Show that if $\lambda \in \sigma(T)$ (spectrum of $T$), then $|\lambda| \leq 1$

Published on 31 Mar 2026 - 15:23

1.4k

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Can every closed subspace be realized as kernel of a bounded linear operator from a Banach space to itself?

Published on 29 Jan 2017 - 20:14

421

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Banach spaces and infinite series

Published on 29 Jan 2017 - 23:26

824

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Does $(\ell^\infty)^*$ have the cardinality of the continuum?

Published on 01 Apr 2026 - 6:33

68

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If $U$ is closed, is Span($U \cup \{z\}$) also closed?

Published on 30 Jan 2017 - 22:12

368

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Closure and convex hull of a set

Published on 31 Jan 2017 - 10:14

36

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In a Banach space, for each point the collection of all scalar multipliers of this point is connected, how to prove?

Published on 02 Apr 2026 - 18:20

146

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How is the Hahn-Banach Theorem being used here?

Published on 01 Feb 2017 - 2:10

29

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Recover a function from the differential map

Published on 28 Mar 2026 - 8:38

396

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Folland Real Analysis 5.2

Published on 05 Feb 2017 - 0:08

182

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Why is this "proof" of the Uniform Boundedness Principle via the contrapositive erroneous?

Published on 05 Feb 2017 - 4:17

List Question

An exercise on a closed graph, functional analysis

Prove a differentiable function between banach spaces is continuous

Prove $C^1([0,1]) $ is Banach.

from weakly convergent sequence to strongly convergent sequence in a non-compact operator

Show that if $\lambda \in \sigma(T)$ (spectrum of $T$), then $|\lambda| \leq 1$

Can every closed subspace be realized as kernel of a bounded linear operator from a Banach space to itself?

Banach spaces and infinite series

Does $(\ell^\infty)^*$ have the cardinality of the continuum?

If $U$ is closed, is Span($U \cup \{z\}$) also closed?

Closure and convex hull of a set

In a Banach space, for each point the collection of all scalar multipliers of this point is connected, how to prove?

How is the Hahn-Banach Theorem being used here?

Recover a function from the differential map

Folland Real Analysis 5.2

Why is this "proof" of the Uniform Boundedness Principle via the contrapositive erroneous?

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