Projectivity of Banach and C*algebras of continuous fields
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 David Cushing
 Dr Zinaida Lykova




Author(s)   Cushing D, Lykova ZA 
Publication type   Article 
Journal   Quarterly Journal of Mathematics 
Year   2013 
Volume   64 
Issue   2 
Pages   341371 
ISSN (print)   00335606 
ISSN (electronic)   14643847 



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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. 



Publisher   Oxford University Press 
URL   http://dx.doi.org/10.1093/qmath/has005 
DOI   10.1093/qmath/has005 

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