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Subspaces of L p , p > 2, determined by partitions and weights

Dale E. AlspachSimei Tong — 2003

Studia Mathematica

Many of the known complemented subspaces of L p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of many well known complemented subspaces of L p . It is proved that the class of spaces with such norms is stable under (p,2) sums. By introducing the notion of an envelope norm, we obtain a necessary condition for a Banach sequence space with norm given by partitions...

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