Completing The Riesz-dunford Functional Calculus (memoirs Of The American Mathematical Society)

Let [script lowercase]f be any analytic function defined in a neighborhood of the non-empty set [italic]E and let [script]S([italic]E) denote the set of all operator having spectrum included in [italic]E. In this paper the closure and interior of the set [script lowercase]f([script]S([italic]E)) ≡ {[script lowercase]f([italic]A): [italic]A ∈[script]S([italic]E)} are characterized. Some applications serve to illustrate the interplay between the analyticity of the functions and the spectral behavior of the operators.588Print version record. Let [script lowercase]f be any analytic function defined in a neighborhood of the non-empty set [italic]E and let [script]S([italic]E) denote the set of all operator having spectrum included in [italic]E. In this paper the closure and interior of the set [script lowercase]f([script]S([italic]E)) [identical equality] {[script lowercase]f([italic]A): [italic]A [set membership] [script]S([italic]E)} are characterized. Some applications serve to illustrate the interplay between the analyticity of the functions and the spectral behavior of the operators John B. Conway, Domingo A. Herrero, And Bernard B. Morrel. November 1989, Volume 82, Number 417 (second Of 3 Numbers) Includes Bibliographical References.