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

 

The Riesz decomposition property for the space of regular operators


Author: Nicolae Danet
Journal: Proc. Amer. Math. Soc. 129 (2001), 539-542
MSC (1991): Primary 47B60; Secondary 47B65, 46B42, 47L05
Published electronically: September 20, 2000
MathSciNet review: 1707144
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Abstract:

If $E$ and $F$ are Banach lattices such that $E$ is separable and $F$ has the countable interpolation property, then the space of all continuous regular operators $\mathcal{L}$$^r(E,F)$ has the Riesz decomposition property. This result is a positive answer to a conjecture posed by A. W. Wickstead.


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Additional Information

Nicolae Danet
Affiliation: Technical University of Civil Engineering of Bucharest, 122-124, Lacul Tei Blvd., 72302 Bucharest, Romania
Email: ndanet@fx.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05592-1
PII: S 0002-9939(00)05592-1
Keywords: Banach lattices, regular operators, Riesz decomposition property
Received by editor(s): December 17, 1998
Received by editor(s) in revised form: May 4, 1999
Published electronically: September 20, 2000
Dedicated: Dedicated to Prof. Romulus Cristescu on his 70th birthday
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society