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This article is cited in 2 scientific papers (total in 2 papers)
Metrically and Topologically Projective Ideals of Banach Algebras
N. T. Nemesh Lomonosov Moscow State University
Abstract:
In the present paper, necessary conditions for the metric and topological projectivity of closed ideals of Banach algebras are given. In the case of commutative Banach algebras, a criterion for the metric and topological projectivity of ideals admitting a bounded approximate identity is obtained. The main result of the paper is as follows: a closed ideal of an arbitrary $C^*$-algebra is metrically or topologically projective if and only if it admits a self-adjoint right identity.
Keywords:
Banach algebra, commutative Banach algebra, metrically projective ideal, topologically projective ideal, self-adjoint right identity.
Received: 08.09.2015
Citation:
N. T. Nemesh, “Metrically and Topologically Projective Ideals of Banach Algebras”, Mat. Zametki, 99:4 (2016), 526–536; Math. Notes, 99:4 (2016), 524–533
Linking options:
https://www.mathnet.ru/eng/mzm10963https://doi.org/10.4213/mzm10963 https://www.mathnet.ru/eng/mzm/v99/i4/p526
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