Full paper in PDF:
$%N. D. Chakraborty and S. Jaker Ali, On strongly Pettis integrable functions in locally convex spaces, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 2, 241262.%$

On Strongly Pettis Integrable Functions in Locally Convex Spaces
N. D. CHAKRABORTY and SkJAKER ALI
Department of Mathematics
University of Burdwan
Burdwan 713 104
West Bengal India

Received: March 27, 1991
Revised: April 15, 1993
ABSTRACT

Some characterizations have been given for the relative compactness of the range of the indefinite Pettis integral of a function on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It has been shown that the indefinite Pettis integral has a relatively compact range if the functions is measurable by seminorm. Separation property has been defined for a scalarly measurable function and it has been proved that a function with this property is integrable by seminorm.

For a bounded function another characterization has been given for the relative compactness of the range of the indefinite Pettis integral. Dunford-Pettis-Phillips theorem has been generalized to locally convex spaces and as a corollary of this theorem some results which are valid for Banach spaces have been extended to locally convex spaces.

1991 Mathematics Subject Classification: 28B05, 46G10.