7 papers · 1 filter
Differentiable, Holomorphic, and Analytic Functions on Complex -Algebras
Mark Roelands, Christopher Michael Schwanke
Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex -algebras. Most notably, we improve the Cauc…
Homogeneous Polynomials: Harmonic Means and Completely Partitioned Weighted Geometric Means
Christopher Schwanke
We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using harmonic means and…
Vector semi-inner products
Kyle Rose, Christopher Schwanke, Zachary Ward
We formalize the notion of vector semi-inner products and introduce a class of vector seminorms which are built from these maps. The classical Pythagorean theorem and parallelogram…
Three geometric constants for Morrey spaces
Hendra Gunawan, Eder Kikianty, Yoshihiro Sawano +1
In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Mo…
Series and power series on universally complete complex vector lattices
Mark Roelands, Christopher Schwanke
In this paper we prove an th root test for series as well as a Cauchy-Hadamard type formula and Abel's' theorem for power series on universally complete Archimedean complex vect…
Characterizing Bounded Orthogonally Additive Polynomials on Vector Lattices
Gerard Buskes, Christopher Schwanke
We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived i…