zbMATH — the first resource for mathematics

An arbitrarily distortable Banach space. (English) Zbl 0796.46007
Summary: In this work we construct a “Tsirelson like Banach space” which is arbitrarily distortable.

46B25 Classical Banach spaces in the general theory
Full Text: DOI arXiv
[1] P. G. Casazza and Th. J. Shura,Tsirelson’s space, Lecture Notes in Math. No. 1363, Springer-Verlag, Berlin, 1989. · Zbl 0709.46008
[2] R. Haydon, E. Odell, H. Rosenthal and Th. Schlumprecht,On distorted norms in Banach spaces and the existence of l p -types, preprint.
[3] R. C. James,Uniformly non-square Banach spaces, Ann. of Math.80 (1964), 542–550. · Zbl 0132.08902 · doi:10.2307/1970663
[4] J. L. Krivine,Sous espaces de dimension finie des espaces de Banach réticulés, Ann. of Math.104 (1976), 1–29. · Zbl 0329.46008 · doi:10.2307/1971054
[5] H. Lemberg,Nouvelle démonstration d’un théorème de J.L. Krivine sum la finie représentation de l p dans un espace de Banach, Isr. J. Math.39 (1981), 341–348. · Zbl 0466.46023 · doi:10.1007/BF02761678
[6] J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces I – Sequence Spaces, Springer-Verlag, Berlin, 1979. · Zbl 0403.46022
[7] V. D. Milman,Geometric theory of Banach spaces, II: Geometry of the unit sphere, Russian Math. Survey26 (1971), 79–163 (translated from Russian). · Zbl 0238.46012 · doi:10.1070/RM1971v026n06ABEH001273
[8] E. Odell, personal communication.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.