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On Banach spaces of regulated functions

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Drewnowski L.

Commentationes Mathematicae

2017

tom 57

nr 2

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 \(K\).

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1 Commentationes Mathematicae

1 Drewnowski L.

1 2017

Wyniki wyszukiwania

On Banach spaces of regulated functions