Uniqueness of unconditional basis in Lorentz sequence spaces
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- by F. Albiac and C. Leránoz PDF
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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.References
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Additional Information
- F. Albiac
- Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, Pamplona 31006, Spain
- MR Author ID: 692748
- ORCID: 0000-0001-7051-9279
- Email: fernando.albiac@unavarra.es
- C. Leránoz
- Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, Pamplona 31006, Spain
- Email: camino@unavarra.es
- Received by editor(s): October 23, 2006
- Published electronically: January 3, 2008
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1643-1647
- MSC (2000): Primary 46A16, 46A35; Secondary 46A40, 46A45
- DOI: https://doi.org/10.1090/S0002-9939-08-09222-8
- MathSciNet review: 2373593