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The Dual of a Non-reflexive L-embedded Banach Space Contains $l^{∞}$ Isometrically

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Pfitzner H.

Bulletin of the Polish Academy of Sciences. Mathematics

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2010

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tom 58

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nr 1

31-38

EN

A Banach space is said to be L-embedded if it is complemented in its bidual in such a way that the norm between the two complementary subspaces is additive. We prove that the dual of a non-reflexive L-embedded Banach space contains $l^{∞}$ isometrically.

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

100%

Pfitzner H.

Studia Mathematica

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1993

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tom 104

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nr 1

91-98

EN

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 $l^1$.

3

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

63%

Peralta A., Pfitzner H.

Studia Mathematica

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2015

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tom 227

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nr 1

77-95

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.

Ograniczanie wyników

2 Studia Mathematica

1 Bulletin of the Polish Academy of Sciences. Mathematics

3 Pfitzner H.

1 Peralta A.

1 2015

1 2010

1 1993

The Dual of a Non-reflexive L-embedded Banach Space Contains $l^{∞}$ Isometrically

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

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