Abel Averages of Holomorphic Mappings

  • David ShoikhetEmail author


We study the geometric and analytic properties of (nonlinear) holomorphic Abel averages defined on Hilbert spaces and \(J^{*}\)-algebras. We show that for pseudo-contractive mappings the Abel averages are well defined and are starlike mappings with respect to the origin of a \(J^{*}\)-algebra. For this reason we also verify some sufficient conditions for holomorphic mappings in Banach spaces to be pseudo-contractive.


Holomorphic mappings Abel averages Pseudo-contractions 

Mathematics Subject Classification

47A12 46G20 46T25 58B12 



Some results of this paper in another context are partially presented in the book [8] and paper [9].


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Authors and Affiliations

  1. 1.Department of MathematicsHolon Institute of TechnologyHolonIsrael

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