On Banach spaces of regulated functions

Lech Drewnowski. "On Banach spaces of regulated functions." Commentationes Mathematicae 57.2 (2017): null. <http://eudml.org/doc/292366>.

@article{LechDrewnowski2017,
abstract = {For a relatively compact subset $S$ of the real line $$, 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 $K$.},
author = {Lech Drewnowski},
journal = {Commentationes Mathematicae},
keywords = {Regulated function; left- and right-continuity; Banach spaces; $c_0(S)$ spaces; triple Sorgenfrey line; Alexandrov--Urysohn constructions; $C(K)$ spaces, isomorphisms},
language = {eng},
number = {2},
pages = {null},
title = {On Banach spaces of regulated functions},
url = {http://eudml.org/doc/292366},
volume = {57},
year = {2017},
}

TY - JOUR
AU - Lech Drewnowski
TI - On Banach spaces of regulated functions
JO - Commentationes Mathematicae
PY - 2017
VL - 57
IS - 2
SP - null
AB - For a relatively compact subset $S$ of the real line $$, 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 $K$.
LA - eng
KW - Regulated function; left- and right-continuity; Banach spaces; $c_0(S)$ spaces; triple Sorgenfrey line; Alexandrov--Urysohn constructions; $C(K)$ spaces, isomorphisms
UR - http://eudml.org/doc/292366
ER -