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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/873B2C00-BA68-421F-B484-E37AD6D28FC6 | ||
| Year | 2001 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | A. Manousakis ,: On the structure of certain class of mixed tsirelson spaces", Pos. ,vol. 5 No.3,pp. 193-238, 2001,doi : 10.1023/A:1011456204116 https://doi.org/10.1023/A:1011456204116 | ||
| Appears in Collections |
We study Banach spaces of the form X=T[(θi,Ani)i=1∞] We call such a space a p-space, p∈[1,∞), if for every k the space T[(θi,Ani)i=1k] is isomorphic to ℓpk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces ℓr in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that θi ni 1/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 c 0 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 ℓ1 embeds into X. We also investigate complemented minimality for the class of spaces T[(θi,Mi)i=1∞] where (Mi) is either a subsequence of the sequence of Schreier classes (S n)n ∈ N or a subsequence of (A n)n ∈ N
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