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# On the Local Lifting Properties of Operator Spaces

Published:2009-12-01
Printed: Dec 2009
• Z. Dong
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## Abstract

In this paper, we mainly study operator spaces which have the locally lifting property (LLP). The dual of any ternary ring of operators is shown to satisfy the strongly local reflexivity, and this is used to prove that strongly local reflexivity holds also for operator spaces which have the LLP. Several homological characterizations of the LLP and weak expectation property are given. We also prove that for any operator space $V$, $V^{**}$ has the LLP if and only if $V$ has the LLP and $V^{*}$ is exact.
 Keywords: operator space, locally lifting property, strongly locally reflexive
 MSC Classifications: 46L07 - Operator spaces and completely bounded maps [See also 47L25]

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