Series and power series on universally complete complex vector lattices

2018/03/21 by Roelands, Mark, Schwanke, Christopher · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1803.07912

Abstract

In this paper we prove an nth root test for series as well as a Cauchy-Hadamard type formula and Abel's' theorem for power series on universally complete Archimedean complex vector lattices. These results are aimed at developing an alternative approach to the classical theory of complex series and power series using the notion of order convergence.

Cited by

• Classical theorems from analysis for locally band preserving functions on Dedekind complete Φ-algebras

Related

• Generalized universal series
• Functional Completions of Archimedean Vector Lattices
• The intermediate value theorem over a non-Archimedean field via Hensel's Lemma
• Completeness for vector lattices
• Power Series in Several Complex Variables