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Projectivity of Banach and C*-algebras of continuous fields

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.

Publication metadata

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


DOI: 10.1093/qmath/has005


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