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

• Autorzy: Antonio M. Peralta , Hermann Pfitzner
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L70: Nonassociative selfadjoint operator algebras
• 46L51: Noncommutative measure and integration
• 46B04: Isometric theory of Banach spaces
• 17C65: Jordan structures on Banach spaces and algebras
• 46B08: Ultraproduct techniques in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 1
• Strony: 77-95

Daty

wydano

2015

Twórcy

autor

Antonio M. Peralta

• Departamento de Análisis Matemático, Universidad de Granada, Facultad de Ciencias, 18071 Granada, Spain
• Department of Mathematics, College of Science, King Saud University, P.O. Box 2455-5, Riyadh 11451, Kingdom of Saudi Arabia

autor

Hermann Pfitzner

• Université d'Orléans, BP 6759, F-45067 Orléans Cedex 2, France

Identyfikatory

DOI

10.4064/sm227-1-5