Nonseparable spaceability and strong algebrability of sets of continuous singular functions
Functional Analysis
2013-01-23 v1
Abstract
Let CBV denote the Banach algebra of all continuous real-valued functions of bounded variation, defined in [0,1]. We show that the set of strongly singular functions in CBV is nonseparably spaceable. We also prove that certain families of singular functions constitute strongly c-algebrable sets. The argument is based on a new general criterion of strong c-algebrability.
Keywords
Cite
@article{arxiv.1301.5162,
title = {Nonseparable spaceability and strong algebrability of sets of continuous singular functions},
author = {Marek Balcerzak and Artur Bartoszewicz and Malgorzata Filipczak},
journal= {arXiv preprint arXiv:1301.5162},
year = {2013}
}