Vol. 55, No. 1, 1974

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Operator valued roots of abelian analytic functions

Frank Larkin Gilfeather

Vol. 55 (1974), No. 1, 127–148

In this paper, all spaces are separable Hilbert spaces and all operators are bounded linear transformations. Questions involving the structure of an operator for which an analytic function of it is normal or which satisfies a polynomial with certain operator coefficients have been considered and studied separately. Using von Neumann’s reduction theory, a unified approach to these and similar questions can be given. This method yields generalizations of the cases which has been previously investigated, including structure results for n. normal operators. Through reduction theory of von Neumann algebras, the study of structural questions for a particular orerator is reduced to the properties of the often simpler, reduced operators. In all of the applications presented in this paper, the reduced operators will simply involve algebraic operators.

Mathematical Subject Classification 2000
Primary: 47A60
Received: 10 April 1973
Revised: 9 January 1974
Published: 1 November 1974
Frank Larkin Gilfeather