Banach Reducibility of Operator Weighted Shifts

Abstract:

      We obtain a necessary and sufficient condition for a unilateral operator weighted shift being BR operator,and gives a sufficient condition for a bilateral operator weighted shiftbeing BR operator,As a consequence,we obtain a corollary in[1] again and a class ofBIR unnateral operator weighted shift.Finally,some unilateral weighted shifts which areboth HIR and BR are shown.