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A universal property of reflexive hereditarily indecomposable Banach spaces

Author(s): Spiros A. Argyros
Journal: Proc. Amer. Math. Soc. 129 (2001), 3231-3239.
MSC (2000): Primary 46B03, 46B70, 46B10; Secondary 03E10, 03E15
Posted: April 16, 2001
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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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R. Neidinger. Properties of Tauberian Operators, Dissertation. University of Texas at Austin, 1984.

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W. Szlenk. The non-existence of a separable reflexive Banach spaces universal for all separable reflexive Banach spaces, Studia Math. 30(1968) 53-61. MR 37:3327

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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: 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
Posted: April 16, 2001
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2001, American Mathematical Society

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