Complex powers of almost C-nonnegative operators

Abstract

In this paper, we construct the complex powers of some classes of closed linear operators including almost C-nonnegative operators and (a, b, C)-nonnegative operators (a, b ∈ R) in the setting of sequentially complete locally convex spaces. A relatively elementary approach which is based on the ideas of A. Balakrishnan [A. V. Balakrishnan, Fractional powers of closed operators and the semigroups generated by them, Pacific J. Math. 10 (2) (1960) 419-437] and C. Martinez, M. Sanz, A. Redondo [C. Martinez, M. Sanz, A. Redondo, Fractional powers of almost nonnegative operators, Fract. Calculus Appl. Anal. 8 (2005) 201-230] will be used. We provide several interesting applications.