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Nonlinear Carleman operators on Banach lattices
Author(s):
William
Feldman
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2109-2115.
MSC (1991):
Primary 46B42, 47H07
Posted:
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.
References:
- 1.
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- 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
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- 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
Email:
wfeldman@comp.uark.edu
DOI:
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
Posted:
March 3, 1999
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1999,
American Mathematical Society
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