N-SUPERCYCLICITY OF AN A-m-ISOMETRY

Abstract

Abstract. An A-m-isometric operator is a bounded linear operator T on a Hilbert space H satisfyingwhere A is a positive operator. We give sufficient conditions under which A-m-isometries are not N -supercyclic, for every N ≥ 1; that is, there is not a subspace E of dimension N such that its orbit under T is dense in H.

Decomposing algebraic m-isometric tuples

“…Let A be a positive operator on H. An operator T is called an (A, m)isometry if it is a solution to the operator equation Such operators were introduced and studied by Sid Ahmed and Saddi in [8], then by other authors [17,25,29,23,19,10]. In the case m = 1, we call such operators A-isometries.…”

“…Such operators were introduced and studied by Sid Ahmed and Saddi in [8], then by other authors [17,25,29,23,19,10]. In the case m = 1, we call such operators A-isometries.…”