Question

Prove a certain property of linear functionals, using the Hahn-Banach-Separation theorems

score 180 · Answer 1 · 2014-12-26 20:30:18

180

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Prove a certain property of linear functionals, using the Hahn-Banach-Separation theorems

Published on 26 Dec 2014 - 20:30

score 168 · Answer 2 · 2014-12-27 03:06:49

168

Views

Gelfand width of $l_1$ unit ball in $\infty$ metric

Published on 27 Dec 2014 - 3:06

score 60 · Answer 3 · 2014-12-30 00:18:27

60

Views

Can there be weak* open cover of the dual banach space with the arbitrary small (in diameter) sets?

Published on 30 Dec 2014 - 0:18

score 209 · Answer 4 · 2015-01-01 15:49:39

209

Views

If Banach space is algebraic sum of its two linear subspaces with mutually separated unit spheres then these subspaces are closed.

Published on 01 Jan 2015 - 15:49

score 424 · Answer 5 · 2015-01-01 17:25:56

424

Views

Is $T(X)$ a Banach space?

Published on 01 Jan 2015 - 17:25

score 556 · Answer 6 · 2026-03-25 08:07:01

556

Views

Why do we consider only real or complex Banach spaces?

Published on 25 Mar 2026 - 8:07

score 923 · Answer 7 · 2019-10-03 08:17:37

923

Views

Does pointwise convergence imply uniform convergence on bounded sets for linear operators?

Published on 03 Oct 2019 - 8:17

score 41 · Answer 8 · 2019-10-03 17:09:27

41

Views

Intersection of linear subspaces is $\{ 0 \}$ iff distance between respective unit vectors is positive in finite dimensions

Published on 03 Oct 2019 - 17:09

score 187 · Answer 9 · 2026-03-27 23:23:30

187

Views

Prove $C[a,b]$ with norm $\Vert f\Vert=\left(\int\limits_{a}^b\vert f(t)\vert^2\right)^{\frac{1}{2}}$ is not Banach space

Published on 27 Mar 2026 - 23:23

score 237 · Answer 10 · 2026-03-30 01:32:06

237

Views

Is possible to show that the linear operator $T(\varphi)(x) = \int_{V_x\cap M} \varphi(y)\text{d}y$ has spectral radius $>0$.

Published on 30 Mar 2026 - 1:32

score 279 · Answer 11 · 2019-10-06 03:21:26

279

Views

Metric on $M[0,1]$ the space of measures

Published on 06 Oct 2019 - 3:21

score 159 · Answer 12 · 2019-10-07 19:11:01

159

Views

Infinite dimensional normed space whose only closed proper subspaces are finite dimensional

Published on 07 Oct 2019 - 19:11

score 101 · Answer 13 · 2019-10-08 08:33:37

101

Views

(Notation/Definition) Little lp on a pointed metric space

Published on 08 Oct 2019 - 8:33

score 1.5k · Answer 14 · 2019-10-08 12:12:29

1.5k

Views

Category of Banach spaces

Published on 08 Oct 2019 - 12:12

score 152 · Answer 15 · 2019-10-08 22:01:37

152

Views

Show that $H_0^1(\Omega) \cap L^p(\Omega)$ is a Banach space

Published on 08 Oct 2019 - 22:01

List Question

Prove a certain property of linear functionals, using the Hahn-Banach-Separation theorems

Gelfand width of $l_1$ unit ball in $\infty$ metric

Can there be weak* open cover of the dual banach space with the arbitrary small (in diameter) sets?

If Banach space is algebraic sum of its two linear subspaces with mutually separated unit spheres then these subspaces are closed.

Is $T(X)$ a Banach space?

Why do we consider only real or complex Banach spaces?

Does pointwise convergence imply uniform convergence on bounded sets for linear operators?

Intersection of linear subspaces is $\{ 0 \}$ iff distance between respective unit vectors is positive in finite dimensions

Prove $C[a,b]$ with norm $\Vert f\Vert=\left(\int\limits_{a}^b\vert f(t)\vert^2\right)^{\frac{1}{2}}$ is not Banach space

Is possible to show that the linear operator $T(\varphi)(x) = \int_{V_x\cap M} \varphi(y)\text{d}y$ has spectral radius $>0$.

Metric on $M[0,1]$ the space of measures

Infinite dimensional normed space whose only closed proper subspaces are finite dimensional

(Notation/Definition) Little lp on a pointed metric space

Category of Banach spaces

Show that $H_0^1(\Omega) \cap L^p(\Omega)$ is a Banach space

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