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 Title: Fractional Powers of Almost Non-Negative Operators Authors: Martínez, CelsoSanz, MiguelRedondo, Antonia Keywords: Fractional PowersNon-Negative OperatorsAlmost Sectorial OperatorsFunctional CalculusSemigroups of Operators47A6047D06 Issue Date: 2005 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Fractional Calculus and Applied Analysis, Vol. 8, No 2, (2005), 201p-230p Abstract: In this paper, we extend the theory of complex powers of operators to a class of operators in Banach spaces whose spectrum lies in C \ ]−∞, 0[ and whose resolvent satisfies an estimate ||(λ + A)^(−1)|| ≤ (λ^(−1) + λ^m) M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operators strictly contains the class of the non negative operators and the one of operators with polynomially bounded resolvent. We also prove that this theory may be extended to sequentially complete locally convex spaces. Description: Mathematics Subject Classification: Primary 47A60, 47D06. URI: http://hdl.handle.net/10525/1254 ISSN: 1311-0454 Appears in Collections: 2005

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