Abstract
One-variable holomorphic functional calculus is studied on the bornological algebra Lec(E) of all continuous linear oprators on a complete locally convex space E. It is proven that the following three basic notions of the theory are equivalent: (i) existence of projective resolvent of an operator T at a point λ0, (ii) strict regularity of λ0 for the operator T in the sense of [12, 13, 15], (iii) tamability of the operator (λ0 − T)−1 (T if λ0 = ∞), which means that there is a new equivalent system of seminorms on E, such that the operator is bounded in each of them.
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Arikan, H., Runov, L. & Zahariuta, V. Holomorphic functional calculus for operators on a locally convex space. Results. Math. 43, 23–36 (2003). https://doi.org/10.1007/BF03322718
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DOI: https://doi.org/10.1007/BF03322718