算子权移位的Banach约化性

Banach Reducibility of Operator Weighted Shifts

本文给出了单边算子权移位是ＢＲ算子的充要条件及双边算子权移位是ＢＲ算子的充分条件．做为推论，重新得到了［１］中的一个结果，并得到了一类ＢＩＲ单边算子权移位的例子。最后，给出大量的ＨＩＲ但同时又是ＢＲ的单边算子权移位。

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.