Isomorphisms and strictly singular operators in mixed Tsirelson spaces

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 TM[(Sn,θn)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 (An)n and (Sn)n.