2018/10/12 by Alikhani, M.
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1810.05638
In this paper, we introduce the concept of a pseudo weakly compact operator of order p between Banach spaces. Also we study the notion of p -Dunford-Pettis relatively compact property which is in "general" weaker than the Dunford-Pettis relatively compact property and gives some characterizations of Banach spaces which have this property. Moreover, by using the notion of p -Right subsets of a dual Banach space, we study the concepts of p -sequentially Right and weak p -sequentially Right properties on Banach spaces. Furthermore, we obtain some suitable conditions on Banach spaces X and Y such that projective tensor and injective tensor products between X and Y have the p -sequentially Right property. Finally, we introduce two properties for the Banach spaces, namely p -sequentially Right ∗ and weak p -sequentially Right ∗ properties and obtain some characterizations of these properties.