Document Type
Lecture
Publication Date
11-20-2014
Abstract
In this talk, we demonstrate how to use convexity to identify specific elements of Archimedean vector lattices that are defined abstractly through functional calculus with more concretely defined elements. Using functional calculus, we then introduce functional completions of Archimedean vector lattices with respect to continuous, real-valued functions on ℝⁿ that are positively homogeneous. Given an Archimedean vector lattice �� and a continuous, positively homogeneous function ℎ on ℝⁿ, the functional completion of �� with respect to ℎ is the smallest Archimedean vector lattice in which one is able to use functional calculus with respect to ℎ. It will also be shown that vector lattice homomorphisms and positive linear maps can often be extended to such completions. Combining all of these concepts, we characterize Archimedean complex vector lattices in terms of functional completions. As an application, we construct the Fremlin tensor product for Archimedean complex vector lattices.
Relational Format
presentation
Recommended Citation
Schwanke, Chris, "Functional Completions and Complex Vector Lattices" (2014). Analysis Seminar. 9.
https://egrove.olemiss.edu/math_analysis/9
