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SOME COMPACTNESS RESULTS IN REAL INTERPOLATION FOR FAMILIES OF BANACH SPACES

Published online by Cambridge University Press:  01 October 1998

MARIÁ J. CARRO  and
JAAK PEETRE
MARIÁ J. CARRO
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain
JAAK PEETRE
Affiliation:
Matematiska Institutionen, Lunds Universitet, S-221 00 Lund, Sweden
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Abstract

The paper shows that, if the operator T[ratio ]A(γ)→B(γ) is compact for almost every γ∈Γ, then T[ratio ]F(Ā)→F([Bmacron]) is compact when F([Xmacron])=(X)SK or F([Xmacron])=(X)SJ is the interpolation functor constructed for infinite families of Banach spaces and S satisfies certain conditions.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 451 - 466
Copyright
The London Mathematical Society 1998

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