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Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean
Authors:Fernando Albiac  Camino Leránoz
Institution:1.Universidad Pública de Navarra,Pamplona,Spain
Abstract:Strongly absolute bases are, roughly speaking, purely nonlocally convex bases in quasi-Banach spaces. When, in addition, they are unconditional then the discrete lattice structure they induce in the space is lattice anti-Euclidean. In this brief note we characterize the complemented unconditional basic sequences in those quasi-Banach spaces with strongly absolute unconditional basis, and use this result to derive the uniqueness of unconditional basis in many classical quasi-Banach spaces.
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