Lifting B-subnormal operators

We study B-operators (Brownian-type operators), which are upper triangular $2\times 2$ block matrix operators with entries satisfying some algebraic constraints. We establish a lifting theorem stating that any B-subnormal operator, i.e., a B-operator with subnormal $(2,2)$ entry, lifts to a B-normal operator, i.e., a B-operator with normal $(2,2)$ entry, where lifting is understood in the sense of extending entries of the block matrices representing the operators in question. The spectral inclusion and the filling-in-holes theorems are obtained for such operators.