Gelfand-Philips and L-limited properties of order P on Banach spaces

Abstract

In this paper we show the stability of the Gelfand-Phillips property of order p under tak- ing injective tensor product, compact operators, and Bochner integrable functions. The concept of L-limited sets of order p; is introduced and some characterizations of limited p-convergent operators are given. Also we define the notion of L-limited property of order p and characterize this property in terms of weak compact operators. Furthermore, we give a new dual characterization of the class of weak* p-convergent operators through L-limited sets of order p: Moreover, some characterizations of the Gelfand-Phillips property of order p in terms of limited p-convergent operators are obtained. In addition by applying our results on the limited p-convergent operators, we obtain some characteriza- tions of the Dunford-Pettis* property of order p. © CSP - Cambridge, UK.