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L-embedded Banach spaces and measure topology

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00131645
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Submitted on : Saturday, February 17, 2007 - 4:14:21 PM
Last modification on : Wednesday, April 8, 2020 - 9:16:08 AM

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Hermann Pfitzner. L-embedded Banach spaces and measure topology. Israël Journal of Mathematics, Hebrew University Magnes Press, 2015, 205, pp.421-451. ⟨hal-00131645⟩

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