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Lookup NU author(s): Dr David Cushing, Dr Zinaida LykovaORCiD
We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify projective $C^*$-algebras $\A$ defined by locally trivial continuous fields $\mathcal{U} = \{\Omega,(A_t)_{t \in \Omega},\Theta\}$ such that each $C^*$-algebra $ A_{t}$ has a strictly positive element. For a commutative $C^*$-algebra $\D$ contained in ${\cal B}(H)$, where $H$ is a separable Hilbert space, we show that the condition of left projectivity of $\D$ is equivalent to the existence of a strictly positive element in $\D$ and so to the spectrum of $\D$ being a Lindel$\ddot{\rm o}$f space.
Author(s): Cushing D, Lykova ZA
Publication type: Article
Publication status: Published
Journal: Quarterly Journal of Mathematics
Year: 2013
Volume: 64
Issue: 2
Pages: 341-371
Print publication date: 19/03/2012
Date deposited: 28/04/2011
ISSN (print): 0033-5606
ISSN (electronic): 1464-3847
Publisher: Oxford University Press
URL: http://dx.doi.org/10.1093/qmath/has005
DOI: 10.1093/qmath/has005
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