Isomorphisms and strictly singular operators in mixed Tsirelson spaces

2011/07/14 by Denka Kutzarova, Kutzarova, Denka, Antonis Manoussakis +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1107.2810

29 pages, no figures

arxiv created 2011/07/14 · arxiv updated 2011/07/15

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[(\mcS_n,θ_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 (\mcA_n)_n and (\mcS_n)_n.

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• Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic