On perfectly homogeneous bases in quasi-Banach spaces
Ver/
Fecha
2009Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1155/2009/865371
Resumen
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) ...
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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. [--]
Materias
Orlicz sequence spaces,
Uniqueness,
Mathematics
Editor
Hindawi Publishing Corporation
Publicado en
Abstract and Applied Analysis, 2009. Article ID 865371, 7 pages
Departamento
Universidad Pública de Navarra. Departamento de Matemáticas /
Nafarroako Unibertsitate Publikoa. Matematika Saila