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

 

Strictly singular non-compact operators on hereditarily indecomposable Banach spaces


Author: I. Gasparis
Journal: Proc. Amer. Math. Soc. 131 (2003), 1181-1189
MSC (2000): Primary 46B03; Secondary 06A07, 03E02
Published electronically: July 26, 2002
MathSciNet review: 1948110
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Abstract: An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic $\ell_1$Banach space. The construction of this operator relies on the existence of transfinite $c_0$-spreading models in the dual of the space.


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Additional Information

I. Gasparis
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-1058
Address at time of publication: Department of Mathematics, University of Crete, Knossou Avenue, P.O. Box 2208, Herakleion, Crete 71409, Greece
Email: ioagaspa@math.okstate.edu, ioagaspa@math.uch.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06657-1
PII: S 0002-9939(02)06657-1
Keywords: Hereditarily Indecomposable space, Tsirelson's space, Schreier sets.
Received by editor(s): July 2, 2001
Received by editor(s) in revised form: November 14, 2001
Published electronically: July 26, 2002
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society