Type and cotype of multilinear operators

Geraldo Botelho, Jamilson R. Campos

Published 2015-02-02Version 1

We introduce the notions of type and cotype of multilinear operators between Banach spaces and the resulting classes of such mappings are studied in the setting of the theory of Banach/quasi-Banach ideals of multilinear operators. Distinctions between the linear and the multilinear theories are pointed out, typical multilinear features of the theory are emphasized and many illustrative examples are provided. The classes we introduce are related to the multi-ideals generated by the linear ideals of operators of some type/cotype and are proved to be maximal and Aron-Berner stable.