This is an announcement for the paper "Disjointly homogeneous rearrangement invariant spaces via interpolation" by Sergey Astashkin.

Abstract: A Banach lattice E is called p-disjointly homogeneous, 1< p< infty, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l_p. Employing methods from interpolation theory, we clarify which rearrangement invariant (r.i.) spaces on [0,1] are p-disjointly homogeneous. In particular, for every 1<p< infty and any increasing concave function f on [0,1], which is not equivalent neither 1 nor t, there exists a p-disjointly homogeneous r.i. space with the fundamental function f. Moreover, in the class of all interpolation r.i. spaces with respect to the Banach couple of Lorentz and Marcinkiewicz spaces with the same fundamental function, dilation indices of which are non-trivial, for every 1<p< infty, there is only a unique p-disjointly homogeneous space.

Archive classification: math.FA

Mathematics Subject Classification: 46E30, 46B03, 46B70

Remarks: 23 pages

Submitted from: astash@samsu.ru

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

http://front.math.ucdavis.edu/1405.0681

or

http://arXiv.org/abs/1405.0681