Strictly singular non-compact operators on hereditarily indecomposable Banach spaces
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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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1181-1189
- MSC (2000): Primary 46B03; Secondary 06A07, 03E02
- DOI: https://doi.org/10.1090/S0002-9939-02-06657-1
- MathSciNet review: 1948110