2011/04/26 by David Cushing, Cushing, David, Zinaida A. Lykova +1
Mathematics · #18G05 #46H25 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:18G05 #msc:46H25
paper · pdf · doi:10.48550/arxiv.1104.4935
34 pages
arxiv created 2011/04/26 · arxiv updated 2011/04/27
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 \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\rm of space.