On a certain class of KσδKσδ Banach spaces

Using a strengthening of the concept of KσδKσδ set, introduced in this paper, we study a certain subclass of the class of KσδKσδ Banach spaces; the so-called strongly KσδKσδ Banach spaces. This class of spaces includes subspaces of strongly weakly compactly generated (SWCG) as well as Polish Banach spaces and it is related to strongly weakly KK-analytic (SWKA) Banach spaces as the known classes of KσδKσδ and weakly KK-analytic (WKA) Banach spaces are related.