Glasgow Mathematical Journal

Table of Contents - May 2012 - Volume 54, Issue 02  

Research Article

SCALAR BOUNDEDNESS OF VECTOR-VALUED FUNCTIONS

MATÍAS RAJAa1 and JOSÉ RODRÍGUEZa2

a1 Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo (Murcia), Spain e-mail: matias@um.es

a2 Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo (Murcia), Spain e-mail: joserr@um.es

Abstract

We provide sufficient conditions for a Banach space-valued function to be scalarly bounded, which do not require to test on the whole dual space. Some applications in vector integration are also given.

(Received September 26 2011)

(Accepted October 03 2011)

(Online publication December 12 2011)

2000 Mathematics Subject Classification

  • 28B05;
  • 46G10

Footnotes

The first author was partially supported by Fundación Séneca (Project 08791/PI/08). The second author was partially supported by MEC and FEDER (Project MTM2008-05396) and Fundación Séneca (Project 08848/PI/08)