Lecture Details
Name: Ray Ryan (NUI Galway)Speaking: Thu 9th May 10:00 - 10:25Title: Banach Lattices in Infinite Dimensional Complex AnalysisAbstract: We trace the influence of vector lattice theory in infinite dimensional holomorphy, starting with the construction by Fremlin in 1972 of a tensor product for Riesz spaces. Fremlin's key result, that every positive bilinear form on $C(K)$ spaces is integral, linked his theory to Grothendieck's work on nuclear and integral operators. We describe recent work by Buskes and others, dealing with regular $m$-homogeneous polynomials on Banach lattices. We look at the concept of orthogonal additivity for $m$-homogeneous polynomials, introduced by Sundaresan in 1991 and we outline some recent results. Finally, we consider holomorphic functions on a complex Banach lattice and we see how the complex lattice structure of the domain can be exploited.