Journal Article

PROJECTIVITY OF BANACH AND C*-ALGEBRAS OF CONTINUOUS FIELDS

David Cushing and Zinaida A. Lykova

in The Quarterly Journal of Mathematics

Volume 64, issue 2, pages 341-371
Published in print June 2013 | ISSN: 0033-5606
Published online March 2012 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/has005
PROJECTIVITY OF BANACH AND C*-ALGEBRAS OF CONTINUOUS FIELDS

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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 𝒰={Ω, (At)t∈Ω, Θ} such that each C*-algebra At has a strictly positive element. For a commutative C*-algebra 𝒟 contained in 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 Lindelöf space.

Journal Article.  0 words. 

Subjects: Pure Mathematics

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