Abstract
Suppose that A is an operator on a Hilbert space H. If λ does not belong to the spectrum of A, then the operator A - λ is invertible; write ρ(λ) = (A - λ)-1. (When it is necessary to indicate the dependence of the function p on the operator A, write ρ = ρ A .) The function ρ is called the resolvent of A. The domain of ρ is the complement of the spectrum of A; its values are operators on H.
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© 1974 Springer-Verlag New York Inc.
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Halmos, P.R. (1974). Spectral radius. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-9976-0_10
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DOI: https://doi.org/10.1007/978-1-4615-9976-0_10
Publisher Name: Springer, New York, NY
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