A new relationship between decomposability and convexity

Bianca Satco

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 457-466
  • ISSN: 0010-2628

Abstract

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In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm · (where f = sup [ a , b ] ⊂ [ 0 , 1 ] ∥ ∫ a b f ( s ) d s ∥ ) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed.

How to cite

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Satco, Bianca. "A new relationship between decomposability and convexity." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 457-466. <http://eudml.org/doc/249887>.

@article{Satco2006,
abstract = {In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm $\left| \left\Vert \cdot \right\Vert \right|$ (where $\left| \left\Vert f\right\Vert \right| =\sup _\{[a,b] \subset [0,1]\} \big \Vert \int _\{a\}^\{b\}f(s) ds \big \Vert $) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed.},
author = {Satco, Bianca},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Pettis integral; decomposable set; convex set; Alexiewicz norm; Pettis integral; decomposable set; convex set; Alexiewicz norm},
language = {eng},
number = {3},
pages = {457-466},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A new relationship between decomposability and convexity},
url = {http://eudml.org/doc/249887},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Satco, Bianca
TI - A new relationship between decomposability and convexity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 457
EP - 466
AB - In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm $\left| \left\Vert \cdot \right\Vert \right|$ (where $\left| \left\Vert f\right\Vert \right| =\sup _{[a,b] \subset [0,1]} \big \Vert \int _{a}^{b}f(s) ds \big \Vert $) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed.
LA - eng
KW - Pettis integral; decomposable set; convex set; Alexiewicz norm; Pettis integral; decomposable set; convex set; Alexiewicz norm
UR - http://eudml.org/doc/249887
ER -

References

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