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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 | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. C. D. Aliprantis and O. Burkinshaw, Positive operators, Academic Press, New York, 1985. MR 87h:47086
  • 2. Sergio Segura De León, Bukhvalov type characterizations of Urysohn operators, Studia Math. 99 (3) (1991), 199-220. MR 92h:47095
  • 3. William Feldman, Carleman operators on Banach lattices, Math. Zeit. 199 (1988), 549-553. MR 90a:47092
  • 4. J. J. Grobler and P. van Eldik, Carleman operators in Riesz spaces, Indag. Math. 45 (4) (1983), 421-433 also Proc. Kon. Ned. Akad. van Wetensh. A 86 (4) (1983). MR 85k:47069
  • 5. J. M. Mazón and S. Segura De León, Order bounded orthogonally additive operators, Rev. Roumaine Math. Pures Appl. 35 (1990), 329-353. MR 92b:47087
  • 6. H. H. Schaefer, Banach lattices and positive operators, Springer, Berlin, 1974. MR 54:11023

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Additional Information

William Feldman
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701

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

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