  In this paper, we study 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 Brownian-type
operator with subnormal $(2,2)$ entry lifts to a Brownian-type 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.
