We introduce a family consisting of invertible matrices with exactly one nonzero entry in each row and each column. The elements of are possibly mutually noncommuting, and they need not be normal or self-adjoint. We consider an operator-valued unilateral weighted shift with a uniformly bounded sequence of weights belonging to , and we describe its minimal reducing subspaces.
"Minimal reducing subspaces of an operator-weighted shift." Ann. Funct. Anal. 8 (4) 531 - 546, November 2017. https://doi.org/10.1215/20088752-2017-0017