4 papers · 1 filter
Holomorphic functions on complex Banach lattices
Christopher Boyd, Raymond A. Ryan, Nina Snigireva
We introduce and study the algebraic, analytic and lattice properties of regular homogeneous polynomials and holomorphic functions on complex Banach lattices. We show that the theo…
Orthogonally Additive Sums of Powers of Linear Functionals
Christopher Boyd, Raymond Ryan, Nina Snigireva
Let be a Banach lattice, non-zero scalars and pairwise independent linear functionals on . We show that if then $\sum_{j=1}^k…
A Nakano Carrier Theorem for Polynomials
Christopher Boyd, Raymond A. Ryan, Nina Snigireva
We use a localisation technique to study orthogonally additive polynomials on Banach lattices. We derive alternative characterisations for orthogonal additivity of polynomials and…
Geometry of Spaces of Orthogonally Additive Polynomials on C(K)
Christopher Boyd, Raymond A. Ryan, Nina Snigireva
We study the space of orthogonally additive -homogeneous polynomials on . There are two natural norms on this space. First, there is the usual supremum norm of uniform con…