On the classes of hereditarily lp Banach spaces

Author： Azimi P.   Ledari A.  

Publisher： Springer Publishing Company

ISSN： 0011-4642

Source： Czechoslovak Mathematical Journal, Vol.56, Iss.3, 2006-09, pp. : 1001-1009

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Abstract

Let X denote a specific space of the class of X α,p Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily lp Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of lp. It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of lp where 1/p + 1/q = 1. For p = 1 it is known that the predual of the Banach space X contains asymptotically isometric copies of c 0. Here we give a direct proof of the known result that X contains asymptotically isometric copies of l1.

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