Abstract
The B-operators (abbreviation for Brownian-type operators) are upper triangular 2 × 2 2\times 2 block matrix operators that satisfy certain algebraic constraints. The purpose of this paper is to characterize the weak, the strong and the uniform stability of B-operators, respectively. This is achieved by giving equivalent conditions for the convergence of powers of a B-operator in each of the corresponding topologies. A more subtle characterization is obtained for B-operators with subnormal ( 2 , 2 ) (2,2) entry. The issue of the strong stability of the adjoint of a B-operator is also discussed.
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