On Banach spaces of regulated functions

• Autorzy: Lech Drewnowski
• Języki publikacji: EN

Abstrakty

EN

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 \(K\).

Słowa kluczowe

EN

Regulated function; left- and right-continuity; Banach spaces; \(c_0(S)\) spaces; triple Sorgenfrey line; Alexandrov--Urysohn constructions; \(C(K)\) spaces, isomorphisms

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2017
• Tom: 57
• Numer: 2

Daty

wydano

2017

online

2018-03-20

Twórcy

autor

Lech Drewnowski

Identyfikatory

DOI

10.14708/cm.v57i2.4373