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Strictly singular non-compact operators on hereditarily indecomposable Banach spaces
Author(s):
I.
Gasparis
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1181-1189.
MSC (2000):
Primary 46B03;
Secondary 06A07, 03E02
Posted:
July 26, 2002
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Additional information
Abstract:
An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic  Banach space. The construction of this operator relies on the existence of transfinite  -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:
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
Posted:
July 26, 2002
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2002,
American Mathematical Society
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