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Distortion and spreading models in modified mixed tsirelson spaces

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dc.contributor.author Argyros, SA en
dc.contributor.author Deliyanni, I en
dc.contributor.author Manoussakis, A en
dc.date.accessioned 2014-03-01T01:18:53Z
dc.date.available 2014-03-01T01:18:53Z
dc.date.issued 2003 en
dc.identifier.issn 0039-3223 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/15246
dc.subject banach space en
dc.subject.classification Mathematics en
dc.subject.other WEAKLY NULL SEQUENCES en
dc.subject.other BANACH-SPACES en
dc.subject.other L(1) en
dc.title Distortion and spreading models in modified mixed tsirelson spaces en
heal.type journalArticle en
heal.identifier.primary 10.4064/sm157-3-1 en
heal.identifier.secondary http://dx.doi.org/10.4064/sm157-3-1 en
heal.language English en
heal.publicationDate 2003 en
heal.abstract The results of the first part concern the existence of higher order l(1) spreading models in asymptotic l(1) Banach spaces. We sketch the proof of the fact that the mixed Tsirelson space T[(S-n, theta(n))(n)], theta(n+m) greater than or equal to theta(n)theta(m) and lim(n) theta(n)(1/n) = 1, admits an l(1)(w) spreading model in every block subspace. We also prove that if X is a Banach space with a basis, with the property that there exists a sequence (theta(n))(n) subset of (0, 1) with lim(n) theta(n)(1/n) = 1, such that, for every n is an element of N, parallel to Sigma(k=1)(m) x(k) parallel to greater than or equal to theta(n) Sigma(k=1)(m) parallel tox(k)parallel to for every S-n-admissable block sequence (x(k))(k=1)(m) of vectors in X, then there exists c > 0 such that every block subspace of X admits, for every n, an en 1 spreading model with constant c. Finally, we give an example of a Banach space which has the above property but fails to admit an l(1)(w) spreading model. In the second part we prove that under certain conditions on the double sequence (k(n),theta(n))(n) the modified mixed Tsirelson space T-M[(S-kn,theta(n))(n)] is arbitrarily distortable. Moreover, for an appropriate choice of (k(n),theta(n))(n), every block subspace admits an l(1)(w) spreading model. en
heal.publisher POLISH ACAD SCIENCES INST MATHEMATICS en
heal.journalName Studia Mathematica en
dc.identifier.doi 10.4064/sm157-3-1 en
dc.identifier.isi ISI:000186451700001 en
dc.identifier.volume 157 en
dc.identifier.issue 3 en
dc.identifier.spage 199 en
dc.identifier.epage 236 en


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