On the Structure of a Certain Class of Mixed Tsirelson Spaces |
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Authors: | Manoussakis A. |
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Affiliation: | (1) Department of Sciences, Section of Mathematics, Technical University of Crete, GR73100 Chania, Greece |
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Abstract: | We study Banach spaces of the form We call such a space a p-space, p [1, ), if for every k the space is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces where is either a subsequence of the sequence of Schreier classes ( n)n N or a subsequence of ( n)n N. |
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