Seán Dineen

Complex Analysis on Infinite Dimensional Spaces

Polynomials * Duality Theory for Polynomials * Holomorphic Mappings Between Locally Convex Spaces * Decompositions of Holomorphic Functions * Riemann Domains * Holomorphic Extensions.

The Second Dual of a JB* Triple System

Summary Using ultrapowers and J * ideals we show that the second dual of a JB * triple system is a JB * triple system. This gives a short proof of a result originally proved in [1].

Complex Geodesics on Convex Domains

Existence and uniqueness of complex geodesics joining two points of a convex bounded domain in a Banach space

Holomorphic Functions on Strong Duals of Fréchet-Montel Spaces

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The approximation property for spaces of holomorphic functions on infinite-dimensional spaces I

are considered. Existence is proved for the unit ball of

Weakly uniformly continuous holomorphic functions and the approximation property

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Convexity in complex analysis

under the assumption that

Entire functions on c0

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Duality Theory for Spaces of Germs and Holomorphic Functions on Nuclear Spaces

is 1-complemented in its double dual. Another existence result for taut domains is also proved. Uniqueness is proved for strictly convex bounded domains in spaces with the analytic Radon-Nikodym property. If the unit ball of

Holomorphic functions on a Banach space

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