Type, cotype and twisted sums induced by complex interpolation

Abstract

This paper deals with extensions or twisted sums of Banach spaces that come induced by complex interpolation and the relation between the type and cotype of the spaces in the interpolation scale and the nontriviality and singularity of the induced extension. The results are presented in the context of interpolation of families of Banach spaces, and are applied to the study of submodules of Schatten classes. We also obtain nontrivial extensions of spaces without the CAP which also fail the CAP.

23 pages; some corrections in the text; removed from section 3 unnecessarily hard proof of known result (also, the case considered in reference [35] seems to cover the interpolation of couples) and changed introduction accordingly; corrected reference and changed paragraph of section 4.3; corrected statement of Theorem 4.4 (same proof)