Series and power series on universally complete complex vector lattices

TL;DR

This paper extends classical series and power series convergence tests to universally complete Archimedean complex vector lattices using order convergence, providing an alternative theoretical framework.

Contribution

It introduces an $n$th root test, Cauchy-Hadamard formula, and Abel's theorem for power series in complex vector lattices, advancing the mathematical foundation in this area.

Findings

Established an $n$th root test for series in complex vector lattices

Derived a Cauchy-Hadamard type formula for power series

Proved Abel's theorem within the context of order convergence

Abstract

In this paper we prove an $n$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 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.