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Matematicheskie Zametki, 2016, Volume 99, Issue 4, Pages 526–536
DOI: https://doi.org/10.4213/mzm10963 (Mi mzm10963) 		 
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
Full-text PDF (492 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10963
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.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-08392
This work was supported by the Russian Foundation for Basic Research under grant no. 15-01-08392.
Received: 08.09.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 4, Pages 524–533
DOI: https://doi.org/10.1134/S0001434616030251
Bibliographic databases:
Document Type: Article
UDC: 517.986.22
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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