[Banach] Abstract of a paper by Richard Lechner and Paul F.X. Mueller

This is an announcement for the paper "Localization and projections on bi--parameter BMO" by Richard Lechner and Paul F.X. Mueller.

Abstract: We prove that for any operator T on bi--parameter BMO the identity factors through T or Id - T. As a consequence, bi--parameter BMO is a primary Banach space. Bourgain's localization method provides the conceptual framework of our proof. It consists in replacing the factorization problem on the non--separable Banach space bi--parameter BMO by its localized, finite dimensional counterpart. We solve the resulting finite dimensional factorization problems by combinatorics of colored dyadic rectangles.

Archive classification: math.FA

Mathematics Subject Classification: 46B25, 60G46, 46B07, 46B26, 30H35

Submitted from: Richard.Lechner@jku.at

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.8786

or

http://arXiv.org/abs/1410.8786