On the stability of the differential process generated by complex interpolation

2017/12/27 by Castillo, Jesús M. F., Corrêa, Willian H. G., Ferenczi, Valentin +1
#46B70 #46E30 #46M18 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1712.09647

Abstract

We study the stability of the differential process of Rochberg and Weiss associated to an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit sphere while there is no (bounded) stability for families of four or more Köthe spaces. In the context or arbitrary pairs of Banach spaces we present local stability results and global isometric stability results.

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