Nuclear elements in Banach Jordan pairs

We introduce nuclear elements in Banach Jordan pairs, generalizing the nuclear elements in Banach algebras. We also define a notion of metric and bounded approximation property in Banach Jordan pairs and show that the trace form Tr introduced in the author's paper "Trace and norm for reduced elements of Jordan pairs" ( Comm. Algebra 25 (1997), 3011-3042) may be extended to the nuclear elements, assuming the bounded approximation property.

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(This paper has appeared in Proceedings of the International Conference on Jordan Structures, Malaga, 1997, pp. 111--117. University of Malaga, 1999)

Ottmar Loos <ottmar.loos@uibk.ac.at>