SUBSPACE MIXING AND UNIVERSALITY CRITERION FOR A SEQUENCE OF OPERATORS

Abstract

Let B(X) denote the algebra of all bounded linear operators on an infinite-dimensional separable complex Banach space X and M be a nonzero subspace of X.  We will characterize properties of being d − M mixing for a N ≥ 2 sequence T_1,j , T_2,j , ... , T_N,j of operators in B(X).  Also, we will give necessary and sufficient conditions for a N ≥ 2 sequence T_1,j , T_2,j , ... , T_N,j of operators in B(X) to satisfy d − M universality criterion in terms of d-M topologically transitivity of this sequence.