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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness of unconditional basis in Lorentz sequence spaces


Authors: F. Albiac and C. Leránoz
Journal: Proc. Amer. Math. Soc. 136 (2008), 1643-1647
MSC (2000): Primary 46A16, 46A35; Secondary 46A40, 46A45
Published electronically: January 3, 2008
MathSciNet review: 2373593
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the Lorentz sequence spaces $ d(\omega,p)$ with $ 0<p<1$ and $ \inf\frac{\omega_1+\cdots+\omega_n}{n^p}>0$ have unique unconditional basis. This completely settles the question of uniqueness of unconditional basis in Lorentz sequence spaces, and solves a problem raised by Popa in 1981 and Nawrocki and Ortyński in 1985.


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Additional Information

F. Albiac
Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, Pamplona 31006, Spain
Email: fernando.albiac@unavarra.es

C. Leránoz
Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, Pamplona 31006, Spain
Email: camino@unavarra.es

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09222-8
PII: S 0002-9939(08)09222-8
Received by editor(s): October 23, 2006
Published electronically: January 3, 2008
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.