Geodesic
On Banach spaces of regulated functions
Commentationes Mathematicae, Tome 57 (2017) no. 2, pp. 153-169.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

For a relatively compact subset \(S\) of the real line \(\BR\), let \(R(S)\) denote the Banach space (under the sup norm) of all regulated scalar functions defined on \(S\). The purpose of this paper is to study those closed subspaces of \(R(S)\) that consist of functions that are left-continuous, right-continuous, continuous, and have a (two-sided) limit at each point of some specified disjoint subsets of \(S\). In particular, some of these spaces are represented as \(C(K)\) spaces for suitable, explicitly constructed, compact spaces \(K\).
DOI : 10.14708/cm.v57i2.4373
Classification : 26A21, 46B20, 46E15, 54D30
Mots-clés : Regulated function, left- and right-continuity, Banach spaces, \(c_0(S)\) spaces, triple Sorgenfrey line, Alexandrov--Urysohn constructions, \(C(K)\) spaces, isomorphisms 
@article{10_14708_cm_v57i2_4373,
     author = {Lech Drewnowski},
     title = {On {Banach} spaces of regulated functions},
     journal = {Commentationes Mathematicae},
     pages = { 153--169},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2017},
     doi = {10.14708/cm.v57i2.4373},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/cm.v57i2.4373/}
}
TY  - JOUR
AU  - Lech Drewnowski
TI  - On Banach spaces of regulated functions
JO  - Commentationes Mathematicae
PY  - 2017
SP  -  153
EP  - 169
VL  - 57
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/cm.v57i2.4373/
DO  - 10.14708/cm.v57i2.4373
LA  - pl
ID  - 10_14708_cm_v57i2_4373
ER  - 
%0 Journal Article
%A Lech Drewnowski
%T On Banach spaces of regulated functions
%J Commentationes Mathematicae
%D 2017
%P  153-169
%V 57
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/cm.v57i2.4373/
%R 10.14708/cm.v57i2.4373
%G pl
%F 10_14708_cm_v57i2_4373
Lech Drewnowski. On Banach spaces of regulated functions. Commentationes Mathematicae, Tome 57 (2017) no. 2, pp.  153-169. doi : 10.14708/cm.v57i2.4373. http://geodesic.mathdoc.fr/articles/10.14708/cm.v57i2.4373/

Cité par Sources :