MINIMAL REDUCING SUBSPACES OF THE UNILATERAL SHIFT

Abstract

We introduce a family T consisting of invertible matrices with exactly one non zero entry in each row and each column. The elements of T are mutually non commuting, and need not be normal or self adjoint. We consider the operator weighted sequence space l 2B (K) with a uniformly bounded weight sequence B = {Bn}∞n=0 in T . For the unilateral shift Son l 2B(K), we obtain a complete description of the reducing and minimal reducing subspaces of S