This is an announcement for the paper "Calderon couples of p-convexified Banach lattices" by Eliran Avni.
Abstract: We deal with the question of whether or not the p-convexified couple (X_0^{(p)},X_1^{(p)}) is a Calderon couple under the assumption that (X_0,X_1) is a Calderon couple of Banach lattices on some measure space. In this preliminary version of the paper we find that the answer is affirmative in the simple case where X_0 and X_1 are sequence spaces and an additional “positivity” assumption is imposed regarding (X_0,X_1). We also prove a quantitative version of the result with appropriate norm estimates. In future versions of this paper we plan to deal with other and more general cases of these results.
Archive classification: math.FA
Mathematics Subject Classification: 46B70, 46E30
Remarks: 7 pages
Submitted from: mcwikel@math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.3238
or