Math @ Duke

Publications [#244028] of Michael C. Reed
Papers Published
 Reed, M; Simon, B, Tensor products of closed operators on Banach spaces,
Journal of Functional Analysis, vol. 13 no. 2
(1973),
pp. 107124, ISSN 00221236
(last updated on 2018/06/17)
Abstract: 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 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. © 1973.


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