This is an announcement for the paper "Isomorphisms and strictly singular operators in mixed Tsirelson spaces" by Denka Kutzarova, Antonis Manoussakis, and Anna Pelczar-Barwacz.

Abstract: We study the family of isomorphisms and strictly singular operators in mixed Tsirelson spaces and their modified versions setting. We show sequential minimality of modified mixed Tsirelson spaces $T_M[(\mc{S}_n,\theta_n)]$ satisfying some regularity conditions and present results on existence of strictly singular non-compact operators on subspaces of mixed Tsirelson spaces defined by the families $(\mc{A}_n)_n$ and $(\mc{S}_n)_n$.

Archive classification: math.FA

Remarks: 29 pages, no figures

Submitted from: amanousakis@isc.tuc.gr

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

http://front.math.ucdavis.edu/1107.2810

or

http://arXiv.org/abs/1107.2810