L-embedded Banach spaces and measure topology

Details L-embedded Banach spaces and measure topology L-embedded Banach spaces and measure topology

2000-03-24

arxiv.org/abs/math/0003154v1

Mathematics

Functional Analysis

Scientific paper

An L-embedded Banach spaace is a Banach space which is complemented in its bidual such that the norm is additive between the two complementary parts. On such spaces we define a topology, called an abstract measure topology, which by known results coincides with the usual measure topology on preduals of finite von Neumann algebras (like $L_1([0,1])$). Though not numerous, the known properties of this topology suffice to generalize several results on subspaces of $L_1([0,1])$ to subspaces of arbitrary L-embedded spaces.

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