Lifting B-subnormal operators

초록

We study B-operators (Brownian-type operators), which are upper triangular 2 x 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.

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