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Journal of Operator Theory

Volume 74, Issue 2, Fall 2015  pp. 249-280.

Parts of adjoint weighted shifts

Authors:  Anders Olofsson
Author institution: Mathematics, Faculty of Science, Centre for\break Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden

Summary:  We characterize the parts of a vector-valued adjoint shift operator using operator inequalities and a stability condition. The characterization applies in a class of weighted shifts containing the classical Hardy shift operator as well as the full scale of standard weighted Bergman shift operators on the unit disc. Related operator models form an integral part in recent work on generalized mathematical systems theory and Bergman inner functions.

Keywords: operator model theory, weighted shift operator, standard weighted Bergman space

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