On the spectra of finite-dimensional perturbations of matrix multiplication operators |
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Authors: | E Azoff K Clancey I Gohberg |
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Institution: | (1) Department of Mathematics, University of Georgia, 30602 Athens, Georgia;(2) Department of Mathematics, Tel Aviv University, Tel Aviv, Israel |
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Abstract: | Let be a closed rectifiable curve and a region in the complex plane. Suppose for each , R() represents multiplication by an nxn-matrix of rational functions and F() is a finite rank operator, both acting on the Hilbert space L
2
n
(). Sufficient conditions are given for the integer valued function dim ker (R()+F()) to be continuous at all but finitely many points in . This result is applied to singular integral operators.This work was partially supported by the National Science Foundation. |
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