Ideals of multilinear functionals. (English) Zbl 0561.47037

Forschungsergeb., Friedrich-Schiller-Univ. Jena 53, 16 p. (1983).
The author generalizes the basic definitions for operator ideals to the setting of multilinear operators. It basically suffices to study ideals of multilinear functionals (definition given in the paper). Some basic examples are given: (weakly) compact, approximable m-functionals. Analogues of the nuclear, integral and absolutely summing operators in the multilinear setting are introduced and discussed. To define the approximation numbers of m-functionals f, one needs a suitable definition of the ”rank of f”. There are several different rather natural possibilities which lead to different notions of approximation numbers. Finally, some results in the Hilbert space setting are discussed.
Reviewer: H.König


47L10 Algebras of operators on Banach spaces and other topological linear spaces
47L05 Linear spaces of operators