Banach spaces and Banach lattices of singular functions
L. Bernal-González, J. Fernández-Sánchez, M. E. Martínez-Gómez, J. B. Seoane-Sepúlveda
Studia Mathematica 260 (2021), 167-193
MSC: Primary 15A03, 46B87; Secondary 26A30, 26B30, 46B42.
DOI: 10.4064/sm200419-7-9
Published online: 2 March 2021
Abstract
The class of real singular functions on the unit interval, that is, those continuous bounded variation functions having null derivative almost everywhere, is studied from the point of view of lineability. In particular, large closed vector subspaces, large linear algebras and large Banach lattices are found to live, except for zero, inside several subclasses of it. These subclasses are related to the size of the zero set, to nowhere monotonicity, or to the existence of noncritical points. Also the family of continuous functions that are constant on full measure sequences of sets is analyzed from this point of view. Moreover, it is studied what happens in this context when one turns from bounded variation topology to uniform convergence topology.
Authors
- L. Bernal-GonzálezDepartamento de Análisis Matemático
Facultad de Matemáticas
Instituto de Matemáticas Antonio de Castro Brzezicki
Universidad de Sevilla
Avenida Reina Mercedes s/n
41080 Sevilla, Spain
e-mail
- J. Fernández-SánchezGrupo de investigación de Teoría
de Cópulas y Aplicaciones
Universidad de Almería
Carretera de Sacramento s/n
04120 Almería, Spain
e-mail
- M. E. Martínez-GómezDepartamento de Análisis Matemático
y Matemática Aplicada
Facultad de Ciencias Matemáticas
Plaza de Ciencias 3
Universidad Complutense de Madrid
28040 Madrid, Spain
e-mail
- J. B. Seoane-SepúlvedaInstituto de Matemática Interdisciplinar (IMI)
Departamento de Análisis Matemático
y Matemática Aplicada
Facultad de Ciencias Matemáticas
Plaza de Ciencias 3
Universidad Complutense de Madrid
28040 Madrid, Spain
e-mail
