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On Some Bergman Shift Operators

Research paper by Olof Giselsson, Anders Olofsson

Indexed on: 27 Jul '10Published on: 27 Jul '10Published in: Complex Analysis and Operator Theory



Abstract

An operator identity satisfied by the shift operator in a class of standard weighted Bergman spaces is studied. We show that subject to a pureness condition this operator identity characterizes the associated Bergman shift operator up to unitary equivalence allowing for a general multiplicity. The analysis of the general case makes contact with the class of n-isometries studied by Agler and Stankus.