Albiac Alesanco, Fernando José

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https://academica-e.unavarra.es/handle/2454/48472

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Albiac Alesanco

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Fernando José

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0001-7051-9279

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88452

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504

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End date: 2009 × Start date: 2009 ×

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    PublicationOpen Access
    The Tsirelson space tau (p) has a unique unconditional basis up to permutation for 0 < p < 1
    (Hindawi Publishing Corporation, 2009) Albiac Alesanco, Fernando José; Leránoz Istúriz, María Camino; Matemáticas; Matematika
    We show that the p-convexified Tsirelson space tau((p)) for 0 < p < 1 and all its complemented subspaces with unconditional basis have unique unconditional basis up to permutation. The techniques involved in the proof are different from the methods that have been used in all the other uniqueness results in the nonlocally convex setting. Copyright (C) 2009 F. Albiac and C. Leranoz.
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    PublicationOpen Access
    On perfectly homogeneous bases in quasi-Banach spaces
    (Hindawi Publishing Corporation, 2009) Albiac Alesanco, Fernando José; Leránoz Istúriz, María Camino; Matemáticas; Matematika
    For 0 < p < infinity the unit vector basis of l(p) has the property of perfect homogeneity: it is equivalent to all its normalized block basic sequences, that is, perfectly homogeneous bases are a special case of symmetric bases. For Banach spaces, a classical result of Zippin (1966) proved that perfectly homogeneous bases are equivalent to either the canonical c(0)-basis or the canonical l(p)-basis for some 1 <= p < infinity. In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases of l(p) for 0 < p < 1 as well amongst bases in nonlocally convex quasi-Banach spaces. Copyright (C) 2009 F. Albiac and C. Leranoz.