Uniqueness of unconditional basis in Lorentz sequence spaces

Albiac, F.; Leránoz, C.

doi:10.1090/S0002-9939-08-09222-8

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
DOI: https://doi.org/10.1090/S0002-9939-08-09222-8
Published electronically: January 3, 2008
MathSciNet review: 2373593
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Abstract: We show that the Lorentz sequence spaces $d(\omega,p)$ with 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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