Sequentially Right-like properties on Banach spaces

Abstract

‎In this paper‎, ‎we first study concept $ p $-sequentially Right property‎, ‎which is $ p$-version of‎

‎the sequentially Right property.\ Also‎,

‎we introduce a new class of subsets of Banach spaces which is called‎

‎$ p$-Right$ ^{\ast} $ set and obtain the relationship between p-Right subsets and p-Right$ ^{\ast} $‎

‎subsets of dual spaces.\ Furthermore‎, ‎for $ 1\leq‎

‎p<q\leq\infty‎, ‎$ we introduce the concepts of‎

‎properties $ (SR)_{p,q}$ and $ (SR^{\ast})_{p,q}$ in order to find a‎

‎condition which every Dunford-Pettis $ q $-convergent operator is Dunford-Pettis $p$-convergent.\ Finally‎, ‎we apply these concepts and obtain‎

‎some characterizations of $ p $-Dunford-Pettis relatively compact property of Banach spaces and their dual spaces‎.