The Perturbation Theory of Some Volterra Operators
نویسنده
چکیده
A general procedure is derived for obtaining sufficient conditions for the similarity of operators T and T + P. This is applied to obtain sharp conditipns for the similarity of the Volterra operators J: f(x)-+ / f(y)dy and J + P where P: f(x) /+/fp(x,y)f(y)dy. By the same methods perturbations of the one sided shift operator S on LP(Ofo) by certain trace class operators P are shown to be similar to S. In the last chapter solvability conditions are obtained for the operator equation TX-XS = A where T and S are normal operators. and attended high school there. He graduated OBK from the University of Florida and attended graduate school in mathematics at the Massachusetts Institute of Technology.
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