Distortion and spreading models in modified mixed tsirelson spaces

Argyros, SA; Deliyanni, I; Manoussakis, A

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