Nonlinear Carleman operators on Banach lattices

Feldman, William

doi:10.1090/S0002-9939-99-04729-2

Nonlinear Carleman operators on Banach lattices
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by William Feldman

Proc. Amer. Math. Soc. 127 (1999), 2109-2115

DOI: https://doi.org/10.1090/S0002-9939-99-04729-2

Published electronically: March 3, 1999

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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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