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Lookup NU author(s): Dr Zinaida LykovaORCiD
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The paper concerns the identification of projective closed ideals of C*-algebras. We prove that, if a C*-algebra has the property that every closed left ideal is projective, then the same is true for all its commutative C*-subalgebras. Further, we say a Banach algebra A is hereditarily projective if every closed left ideal of A is projective. As a corollary of the stated result we show that no infinite-dimensional AW*-algebra is hereditarily projective. We also prove that, for a commutative C*-algebra A contained in B(H), where H is a separable Hilbert space, the following conditions are equivalent: (i) A is separable; and (ii) the C*-tensor product A circle times(min) A is hereditarily projective. Howerever, there is a non-separable, hereditarily projective, commutative C*-algebra A contained in B(H), where H is a separable Hilbert space.
Author(s): Lykova ZA
Publication type: Article
Publication status: Published
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
ISSN (print): 0305-0041
ISSN (electronic): 1469-8064
Publisher: Cambridge University Press
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