Bezout operators for analytic operator functions. I: A general concept of Bezout operator. (English) Zbl 0824.47012
Summary: The notion of Bezout operator, previously known for some special classes of scalar entire functions and for matrix and operator polynomials, is introduced for general analytic operator functions. Our approach is based on representing the operator functions involved in realized form. Basic properties of Bezout operators are established and known Bezout operators are shown to be specific realizations of our general concept.
MSC:
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
| 93B28 | Operator-theoretic methods |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 12D10 | Polynomials in real and complex fields: location of zeros (algebraic theorems) |
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