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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A universal property of reflexive hereditarily indecomposable Banach spaces


Author: Spiros A. Argyros
Journal: Proc. Amer. Math. Soc. 129 (2001), 3231-3239
MSC (2000): Primary 46B03, 46B70, 46B10; Secondary 03E10, 03E15
Published electronically: April 16, 2001
MathSciNet review: 1844998
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Abstract:

It is shown that every separable Banach space $X$ universal for the class of reflexive Hereditarily Indecomposable space contains $C[0,1]$ isomorphically and hence it is universal for all separable spaces. This result shows the large variety of reflexive H.I. spaces.


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Additional Information

Spiros A. Argyros
Affiliation: Department of Mathematics, Athens University, Athens, Greece
Address at time of publication: Department of Mathematics, National Technical University of Athens, Athens 15780, Greece
Email: sargyros@math.uoa.gr, sargyros@math.ntua.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05980-9
PII: S 0002-9939(01)05980-9
Keywords: Reflexive Banach spaces, hereditarily indecomposable Banach spaces, universal Banach spaces, well-founded trees
Received by editor(s): March 5, 2000
Published electronically: April 16, 2001
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2001 American Mathematical Society