List questions from banach-spaces

Published on 11 Apr 2026 - 4:56

278

Views

If $X$ is separable, then $\mathcal{F}(X)$ is also separable, where $\mathcal{F}(X) = \overline{span \{ \delta_x : x \in X \}}$

Published on 03 Nov 2015 - 8:48

160

Views

Structure of a set whose image through continuous convex functions is an interval

Published on 03 Nov 2015 - 19:38

323

Views

Extension of a linear map

Published on 29 Mar 2026 - 22:27

198

Views

Show that a function is nowhere Gateaux differentiable.

Published on 25 Mar 2026 - 21:24

92

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Functional characterization of the boundary of a convex set

Published on 04 Nov 2015 - 14:12

179

Views

Separability of $l_p(I,K)$

Published on 04 Nov 2015 - 14:46

3.6k

Views

Norm of product of linear operators in normed vector space

Published on 04 Nov 2015 - 19:30

95

Views

show that $(y^* \circ F) * \gamma(x) = \int_X {y^* \circ F(x+t)}d\gamma(t)$ is Gateaux differentiable everywhere

Published on 05 Nov 2015 - 1:20

66

Views

Definition of $\nabla f(ux_n - S(t))$ on a Banach space

Published on 06 Apr 2026 - 6:17

414

Views

Show that a positive homogeneous uniform continuous map is Lipschitz

Published on 29 Mar 2026 - 22:28

241

Views

Show that $T^$ is weak$^$-to-weak$^*$ continuous

Published on 06 Nov 2015 - 2:45

60

Views

Existence of extension from a subspace to whole space

Published on 28 Mar 2026 - 12:19

181

Views

Norm of linear operator

Published on 09 Apr 2026 - 9:08

140

Views

Show that any convex subset of a Banach space X is closed with respect to the norm if and only if it is closed in the weak topology

Published on 30 Mar 2026 - 14:25

List Question

Continuous linear bijection of a Banach space is a homeomorphism

If $X$ is separable, then $\mathcal{F}(X)$ is also separable, where $\mathcal{F}(X) = \overline{span \{ \delta_x : x \in X \}}$

Structure of a set whose image through continuous convex functions is an interval

Extension of a linear map

Show that a function is nowhere Gateaux differentiable.

Functional characterization of the boundary of a convex set

Separability of $l_p(I,K)$

Norm of product of linear operators in normed vector space

show that $(y^* \circ F) * \gamma(x) = \int_X {y^* \circ F(x+t)}d\gamma(t)$ is Gateaux differentiable everywhere

Definition of $\nabla f(ux_n - S(t))$ on a Banach space

Show that a positive homogeneous uniform continuous map is Lipschitz

Show that $T^$ is weak$^$-to-weak$^*$ continuous

Existence of extension from a subspace to whole space

Norm of linear operator

Show that any convex subset of a Banach space X is closed with respect to the norm if and only if it is closed in the weak topology

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