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A class of Banach sequence spaces analogous to the space of Popov

Parviz AzimiA. A. Ledari — 2009

Czechoslovak Mathematical Journal

Hagler and the first named author introduced a class of hereditarily l 1 Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily l p Banach spaces for 1 p < . Here we use these spaces to introduce a new class of hereditarily l p ( c 0 ) Banach spaces analogous of the space of Popov. In particular, for p = 1 the spaces are further examples of hereditarily l 1 Banach spaces failing the Schur property.

On the classes of hereditarily p Banach spaces

Parviz AzimiA. A. Ledari — 2006

Czechoslovak Mathematical Journal

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 p Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of p . It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of q 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...

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