Bulletin of the Belgian Mathematical Society - Simon Stevin

Almost summability and unconditionally Cauchy series

A. Aizpuru, R. Armario, and F.J. Pérez-Fernández

Full-text: Open access

Abstract

In this paper, we obtain new characterizations of weakly unconditionally Cauchy series and unconditionally convergent series through the summability obtained by the Banach-Lorentz convergence. We study new spaces associated to a series in a Banach space and obtain a new version of the Orlicz-Pettis theorem by means of the almost summability.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 4 (2008), 635-644.

Dates
First available in Project Euclid: 5 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1225893944

Digital Object Identifier
doi:10.36045/bbms/1225893944

Mathematical Reviews number (MathSciNet)
MR2475488

Zentralblatt MATH identifier
1166.46004

Subjects
Primary: 46B15: Summability and bases [See also 46A35]
Secondary: 40A05: Convergence and divergence of series and sequences 46B45: Banach sequence spaces [See also 46A45]

Citation

Aizpuru, A.; Armario, R.; Pérez-Fernández, F.J. Almost summability and unconditionally Cauchy series. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 4, 635--644. doi:10.36045/bbms/1225893944. https://projecteuclid.org/euclid.bbms/1225893944


Export citation