Completing the Riesz-Dunford Functional Calculus

John B. Conway · Domingo A. Herrero · Bernard B. Morrel

Jan 1989 · American Mathematical Society: Memoirs of the American Mathematical Society Buku 417 · American Mathematical Soc.

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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.