A universal property of reflexive hereditarily indecomposable Banach spaces

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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2001-11, Vol.129 (11), p.3231-3239
Main Author: Argyros, Spiros A.
Format: Article
Language:English
Subjects:
Banach space
Mathematical theorems
Property titles
Separable spaces
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Description
Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-01-05980-9