Series and power series on universally complete complex vector lattices

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 se...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-05, Vol.473 (2), p.680-694, Article 680
Main Authors: Roelands, M., Schwanke, C.
Format: Article
Language:English
Subjects:
Complex analysis
Complex vector lattice
Order convergence
Power series
Series
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.12.041