Abstract
The so-called J *-algebras, introduced by L.A. Harris, are closed subspaces of the space L(H) of bounded linear operators over a Hilbert space H which preserves a kind of Jordan triple product structure. The open unit ball of any J *-algebra is a natural generalization of the open unit disk in the complex plane. In particular, any C *-algebra can be realized as a J *-algebra.
In turn, the problems related to the stability of solutions to automorphic differential equations under perturbations can be often transformed to the geometric function theory study on J *-algebras.
In this direction we solve some radii problems for holomorphically accretive mappings acting in the unit ball of a unital J *-algebra.
We also characterize a class of biholomorphic mappings having a symmetrically- spiral structure.
Mathematics Subject Classification (2010). Primary 46G20; Secondary 46H30
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© 2016 Springer International Publishing Switzerland
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Elin, M., Shoikhet, D. (2016). The Radii Problems for Holomorphic Mappings in J*-algebras. In: Alpay, D., Cipriani, F., Colombo, F., Guido, D., Sabadini, I., Sauvageot, JL. (eds) Noncommutative Analysis, Operator Theory and Applications. Operator Theory: Advances and Applications(), vol 252. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29116-1_10
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DOI: https://doi.org/10.1007/978-3-319-29116-1_10
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-29114-7
Online ISBN: 978-3-319-29116-1
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