The Radii Problems for Holomorphic Mappings in J*-algebras
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.
KeywordsHolomorphically dissipative mapping spirallike mapping J*-algebra leaf-composed domain
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