Complutense University Library

On Denjoy-Dunford and Denjoy-Pettis integrals.

Gámez Merino, José Luis and Mendoza Casas, José (1998) On Denjoy-Dunford and Denjoy-Pettis integrals. Studia Mathematica, 130 (2). 115-133 . ISSN 0039-3223

[img] PDF
Restricted to Repository staff only until 31 December 2020.

858kB

Official URL: http://matwbn.icm.edu.pl/ksiazki/sm/sm130/sm13023.pdf

View download statistics for this eprint

==>>> Export to other formats

Abstract

The two main results of this paper are the following: (a) If X is a Banach space and f : [a, b] --> X is a function such that x*f is Denjoy integrable for all x* is an element of X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function f : [a, b] --> c(0) which is not Pettis integrable on any subinterval in [a, b], while integral(J)f belongs to co for every subinterval J in [a, b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dunford and Denjoy-Pettis integrals are studied.


Item Type:Article
Uncontrolled Keywords:Banach-valued functions; Denjoy-Dunford integrals; Denjoy-Pettis integrals
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15426
References:

J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, 1984.

J. Diestel and J. J. Uhl, JI.) Vector Measu.res, Math. Surveys 15, Amer. Math. Soc., 1977.

J N. Dunford and J. T. S chwartz, Linear Operators, Part J, Interscience, New York, 1958.

R. A. Gordoll, The Denjoy extension Di the Bochner, Pettis, and Dunford integrals, Studia Math. 92 (1989), 73-91.

The integrals 01 Lebesgue, Denjoy, Perron and Henstock, Grad. Stud. Math. 4, Amer. Math. Soc" Providence, 1994.

J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces J, Springer, 1977.

S. Saks, Theory 01 the Integral, 2nd revised ed.) Hafner, New York, 1937.

Deposited On:30 May 2012 08:07
Last Modified:06 Feb 2014 10:24

Repository Staff Only: item control page