2108

Some classes of p-convergent operators with weakly p-summable sequences on Banach lattices

دكتري تخصصي

رياضي محض گرايش آناليز

مركز تحصيلات تكميلي دانشگاه پيام نور

1403

1403/06/25

دكتر حليمه اردكاني

دكتر صديقه شادكام

almost limited set, almost Dunford-pettis set, weakly p-compact set, weakly p-summable sequence, p-Schur property, Gelfand-Phillips property, p-convergent operator

The purpose of this thesis is to introduce and study the class of almost limited p-convergent, almost Dunford-pettis p-convergent, weak almost p-convergent and weak almost p- convergent operators on Banach lattices (1 p < 1). Some new characterizations of Banach lattices with the strong limited p-Schur property; that is, spaces on which every almost limited weakly p-compact set is relatively campact and weak DP property of order p are obtained. The behavior of the class of these operators with the weak DP property of order p (with focus on Banach lattics with the strong limited p-Schur property) is investigated. Moreover, Banach lattices with the positive limited p-Schur property are introduced and Banach lattices in which this property is equivalent to some other known properties of almost limited p-convergent, almost Dunford-pettices p-convergent, weak almost p-convergent and weak almost p-convergent operators are considered. As an application, using almost limited p-convergent operators, we establish some necessary and sufficient conditions under which some operator spaces have the strong limited p-Schur property.

1403/10/16

ابراهيمي

77211