List questions from banach-spaces

Published on 27 Mar 2026 - 7:18

64

Views

Prove that $(X,||.||_0)$ is banach space. where $||x||_0=||y||+||z||$

Published on 19 Nov 2019 - 18:53

225

Views

Inclusion of Lorentz Space

Published on 20 Nov 2019 - 0:33

196

Views

Definition of Gelfand width

Published on 20 Nov 2019 - 10:51

50

Views

Homeomorphisms between infinite dimensional planes and spheres

Published on 20 Nov 2019 - 17:08

60

Views

The Exponential Construction in Banach Spaces

Published on 21 Nov 2019 - 16:13

812

Views

Showing Global Lipschitz $\implies$ Global Solution ODE

Published on 26 Mar 2026 - 16:02

32

Views

Why sequences exist in function spaces(and more general spaces) eg. f_n in C[0,1]

Published on 24 Nov 2019 - 21:33

122

Views

$\sum\limits_{j=1}^\infty x_n(j)y(j)\rightarrow0$ for every $y\in l^q$ iff $\sup\{\|x_n\|: n\geq1\}<\infty$ and $x_n(j)\to0$ for $j\geq1$

Published on 25 Nov 2019 - 1:04

1.1k

Views

Is it possible to generalize Taylor's theorem on Banach spaces to the case function is differentiable at just one point?

Published on 25 Nov 2019 - 11:39

376

Views

Sequence of continuously differentiable functions

Published on 26 Nov 2019 - 12:34

1.1k

Views

Prove an operator is injective

Published on 27 Nov 2019 - 3:56

62

Views

Which collections $\{g_n\}$ of continuous functions satisfy $\int_{0}^{1} f \cdot g_n = 0$ implies $f \equiv 0$ for any continuous $f$?

Published on 31 Mar 2026 - 4:00

163

Views

Define a norm using a metric instead of the other way around

Published on 28 Nov 2019 - 11:56

299

Views

Weak convergence in uniformly convex spaces

Published on 28 Nov 2019 - 12:23

List Question

Is the space of smooth functions dense in that of continuous ones?

Prove that $(X,||.||_0)$ is banach space. where $||x||_0=||y||+||z||$

Inclusion of Lorentz Space

Definition of Gelfand width

Homeomorphisms between infinite dimensional planes and spheres

The Exponential Construction in Banach Spaces

Showing Global Lipschitz $\implies$ Global Solution ODE

Why sequences exist in function spaces(and more general spaces) eg. f_n in C[0,1]

$\sum\limits_{j=1}^\infty x_n(j)y(j)\rightarrow0$ for every $y\in l^q$ iff $\sup\{\|x_n\|: n\geq1\}<\infty$ and $x_n(j)\to0$ for $j\geq1$

Is it possible to generalize Taylor's theorem on Banach spaces to the case function is differentiable at just one point?

Sequence of continuously differentiable functions

Prove an operator is injective

Which collections $\{g_n\}$ of continuous functions satisfy $\int_{0}^{1} f \cdot g_n = 0$ implies $f \equiv 0$ for any continuous $f$?

Define a norm using a metric instead of the other way around

Weak convergence in uniformly convex spaces

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