List questions from banach-spaces

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Let $V:= (C([0,1]),\|\cdot\|$) with $\|f\|:= \int_0^1|f(x)| \ dx$. Consider the function $f_n$ and show that V is not a Banach Space.

Published on 27 Mar 2026 - 5:41

3.5k

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Resolvent: Definition

Published on 27 Mar 2026 - 15:16

270

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Convergence of the sequence of operators on a Banach space.

Published on 26 Mar 2026 - 9:49

75

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Inequality norms

Published on 26 Mar 2026 - 11:16

482

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Existence of nontrivial bounded linear operator?

Published on 31 May 2014 - 15:08

1k

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Compact Operators: Separable Range

Published on 31 May 2014 - 17:09

1.1k

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What makes compact operators special?

Published on 26 Mar 2026 - 9:25

525

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Fredholm Index: Finite Corank $\Rightarrow$Closed Range

Published on 26 Mar 2026 - 9:16

68

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Dual space of $L^2(0,T;H^1) + L^p(0,T;L^p)$ and its duality pairing?

Published on 02 Jun 2014 - 21:18

451

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Functional defined on the space of functions with compact support

Published on 25 Mar 2026 - 20:09

166

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If $P$ has marginals $P_1, P_2$, is $L^1(P_1) + L^1(P_2)$ closed in $L^1(P)$?

Published on 03 Jun 2014 - 14:08

87

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Simple question about convergence and Gateaux derivative

Published on 27 Mar 2026 - 16:57

981

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Operator: not closable!

Published on 27 Mar 2026 - 15:16

112

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Complexity of a Borel linear subspace of a Banach space

Published on 25 Mar 2026 - 22:04

73

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uniform continuity of the function $t\mapsto\langle x^*,f(t)\rangle$

Published on 28 Mar 2026 - 9:45

List Question

Let $V:= (C([0,1]),\|\cdot\|$) with $\|f\|:= \int_0^1|f(x)| \ dx$. Consider the function $f_n$ and show that V is not a Banach Space.

Resolvent: Definition

Convergence of the sequence of operators on a Banach space.

Inequality norms

Existence of nontrivial bounded linear operator?

Compact Operators: Separable Range

What makes compact operators special?

Fredholm Index: Finite Corank $\Rightarrow$Closed Range

Dual space of $L^2(0,T;H^1) + L^p(0,T;L^p)$ and its duality pairing?

Functional defined on the space of functions with compact support

If $P$ has marginals $P_1, P_2$, is $L^1(P_1) + L^1(P_2)$ closed in $L^1(P)$?

Simple question about convergence and Gateaux derivative

Operator: not closable!

Complexity of a Borel linear subspace of a Banach space

uniform continuity of the function $t\mapsto\langle x^*,f(t)\rangle$

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