Abstract
A study of 3-isometries on a Hilbert space H which have 3-Brownian unitary extensions is developed. It was inspired by the similar results of Agler-Stankus in the context of 2-isometries. We give matrix representations for these operators and for theirs Brownian type extensions, as well as for the taut extensions in this context. A useful description of such an operator T is obtained in terms of a characteristic polynomial associated to T.
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