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

 

Nonlinear Carleman operators
on Banach lattices


Author: William Feldman
Journal: Proc. Amer. Math. Soc. 127 (1999), 2109-2115
MSC (1991): Primary 46B42, 47H07
Published electronically: March 3, 1999
MathSciNet review: 1485472
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Abstract: An operator, not necessarily linear, will be called a Carleman operator if the image of the positive elements in the unit ball are bounded in the universal completion of the range space. For certain Banach lattices, a class of (not necessarily linear) Carleman operators is characterized in terms of an integral representation and in a more general setting as operators satisfying a pointwise finiteness condition. These operators though not linear are orthogonally additive and monotone.


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Additional Information

William Feldman
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: wfeldman@comp.uark.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04729-2
PII: S 0002-9939(99)04729-2
Received by editor(s): December 9, 1996
Received by editor(s) in revised form: October 16, 1997
Published electronically: March 3, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society