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Cobos, Fernando; Fernández-Cabrera, Luz M.; Martínez, Antón
Nonlinear analysis, October 2020, 2020-10-00, 20201001, Letnik: 199Journal Article
Let Ā=(A0,A1), B̄=(B0,B1) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ‖T(a,b)‖E≤Mj‖a‖Aj‖b‖Bj for a∈A0∩A1, b∈B0∩B1, j=0,1. If T:Aj∘×Bj∘⟶E compactly for j=0 or 1, we show that T may be uniquely extended to a compact bilinear operator from the complex interpolation spaces generated by Ā and B̄ to E. Furthermore, the corresponding result for the real method is given and we also study the case when E is replaced by a couple (E0,E1) of Banach function spaces on the same measure space.
