DP1 AND COMPLETELY CONTINUOUS OPERATORS

W. Freedman introduced an alternate to the Dunford‐Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞ , has the DP1 property if and only if each X α does. This is not the case for . In fact, we show that has the DP1 property if and only if it has the Dunford‐Pettis pr...

Full description

Saved in:

Bibliographic Details
Published in:	International Journal of Mathematics and Mathematical Sciences Vol. 2003; no. 37; pp. 2375 - 2378-180
Main Authors:	Bator, Elizabeth M., Slavens, Dawn R.
Format:	Journal Article
Language:	English
Published:	Hindawi Limiteds 2003 Wiley
ISSN:	0161-1712, 1687-0425
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	W. Freedman introduced an alternate to the Dunford‐Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞ , has the DP1 property if and only if each X α does. This is not the case for . In fact, we show that has the DP1 property if and only if it has the Dunford‐Pettis property. A similar result also holds for vector‐valued continuous function spaces.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0161-1712 1687-0425
DOI:	10.1155/S0161171203302315