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L-summands in their biduals have Pełczyński's property (V*)

Hermann Pfitzner — 1993

Studia Mathematica

Banach spaces which are L-summands in their biduals - for example l 1 , the predual of any von Neumann algebra, or the dual of the disc algebra - have Pełczyński’s property (V*), which means that, roughly speaking, the space in question is either reflexive or is weakly sequentially complete and contains many complemented copies of l 1 .

The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals

Antonio M. PeraltaHermann Pfitzner — 2015

Studia Mathematica

Any bounded sequence in an L¹-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec-Pełczyński-Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW*-algebras. In this note we generalize it to JBW*-triple preduals.

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