Projectivity of Banach and C*-algebras of continuous fields

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  2. David Cushing
  3. Dr Zinaida Lykova
Author(s)Cushing D, Lykova ZA
Publication type Article
JournalQuarterly Journal of Mathematics
ISSN (print)0033-5606
ISSN (electronic)1464-3847
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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.
PublisherOxford University Press
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