This is an announcement for the paper "Complex interpolation of compact operators mapping into lattice couples" by Michael Cwikel.

Abstract: Suppose that (A_0,A_1) and (B_0,B_1) are Banach couples, and that T is a linear operator which maps A_0 compactly into B_0 and A_1 boundedly (or even compactly) into B_1. Does this imply that T maps [A_0,A_1]_s to [B_0,B_1]_s compactly for 0<s<1 ? (Here, as usual, [A_0,A_1]_s denotes the complex interpolation space of Alberto Calderon.) This question has been open for 44 years. Affirmative answers are known for it in many special cases. We answer it affirmatively in the case where (A_0,A_1) is arbitrary and (B_0,B_1) is a couple of Banach lattices having absolutely continuous norms or the Fatou property.

Archive classification: math.FA

Mathematics Subject Classification: 46B70, 46E30 (primary)

Remarks: 14 pages. (Page 13 contains routine and standard material which you

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http://arXiv.org/abs/0802.3520

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