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
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by F. Albiac and C. Leránoz PDF

Proc. Amer. Math. Soc. 136 (2008), 1643-1647 Request permission

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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