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Publications [#244028] of Michael C. Reed

Papers Published

  1. Reed, M; Simon, B, Tensor products of closed operators on Banach spaces, Journal of Functional Analysis, vol. 13 no. 2 (1973), pp. 107-124, ISSN 0022-1236
    (last updated on 2017/12/13)

    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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