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Abel Averages of Holomorphic Mappings

  • David ShoikhetEmail author
Article
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Abstract

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.

Keywords

Holomorphic mappings Abel averages Pseudo-contractions 

Mathematics Subject Classification

47A12 46G20 46T25 58B12 

Notes

Acknowledgements

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

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHolon Institute of TechnologyHolonIsrael

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