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Tensor products of closed operators on Banach spaces

By Michael Reed and Barry Simon

Abstract

AbstractLet 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 α 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 ⊗ B where A and B are the generators of bounded holomorphic semigroups

Publisher: Published by Elsevier Inc.
Year: 1973
DOI identifier: 10.1016/0022-1236(73)90038-4
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