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Projectivity of Banach and C*-algebras of continuous fields
Lookup NU author(s)
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
341-371
ISSN (print)
0033-5606
ISSN (electronic)
1464-3847
Full text is available for this publication:
Full text file 1
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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