Geodesic
Metrically and Topologically Projective Ideals of Banach Algebras
Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 526-536

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2016_99_4_a4,
     author = {N. T. Nemesh},
     title = {Metrically and {Topologically} {Projective} {Ideals} of {Banach} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {526--536},
     publisher = {mathdoc},
     volume = {99},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a4/}
}
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N. T. Nemesh. Metrically and Topologically Projective Ideals of Banach Algebras. Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 526-536. http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a4/