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APPROXIMATELY MULTIPLICATIVE DECOMPOSITIONS OF NUCLEAR MAPS

Part of: Selfadjoint operator algebras Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 July 2021

DOUGLAS WAGNER Open the ORCID record for DOUGLAS WAGNER [Opens in a new window]
DOUGLAS WAGNER*
Affiliation:
Department of Mathematics, Texas Christian University, Fort Worth, Texas, USA
*
e-mail: [email protected]
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Abstract

We expand upon work from many hands on the decomposition of nuclear maps. Such maps can be characterised by their ability to be approximately written as the composition of maps to and from matrices. Under certain conditions (such as quasidiagonality), we can find a decomposition whose maps behave nicely, by preserving multiplication up to an arbitrary degree of accuracy and being constructed from order-zero maps (as in the definition of nuclear dimension). We investigate these conditions and relate them to a W*-analogue.

Keywords

nuclearexactCPAPorder zeroquasidiagonal

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L45: Decomposition theory for $C^*$-algebras 46B28: Spaces of operators; tensor products; approximation properties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 2 , April 2022 , pp. 314 - 322
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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