Tensor Products of Closed Operators on Banach Spaces
نویسندگان
چکیده
Let A and B be closed operators on Banach spaces X and Y. Assume that A and B have nonempty resolvent sets and that the spectra of A and B are unbounded. Let 01 be a uniform cross norm on X @ Y. Using the Gelfand theory and resolvent algebra techniques, a spectral mapping theorem is proven for a certain class of rational functions of A and B. The class of admissable rational functions (including polynomials) depends on the spectra of A and B. The theory is applied to the cases A @ I + I @ B and A 0 B where A and B are the generators of bounded holomorphic semigroups.
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تاریخ انتشار 1972