Characteristic Functions of Liftings

Details Characteristic Functions of Liftings Characteristic Functions of Liftings

2007-07-10

arxiv.org/abs/0707.1417v1

Mathematics

Operator Algebras

31 pages

Scientific paper

We introduce characteristic functions for certain contractive liftings of row contractions. These are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model. The most important cases are subisometric and coisometric liftings. We also identify the most general setting which we call reduced liftings. We derive properties of these new characteristic functions and discuss the relation to Popescu's definition for completely non-coisometric row contractions. Finally we apply our theory to completely positive maps and prove a one-to-one correspondence between the fixed point sets of completely positive maps related to each other by a subisometric lifting.

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