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/}
}
TY  - JOUR
AU  - N. T. Nemesh
TI  - Metrically and Topologically Projective Ideals of Banach Algebras
JO  - Matematičeskie zametki
PY  - 2016
SP  - 526
EP  - 536
VL  - 99
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a4/
LA  - ru
ID  - MZM_2016_99_4_a4
ER  - 
%0 Journal Article
%A N. T. Nemesh
%T Metrically and Topologically Projective Ideals of Banach Algebras
%J Matematičeskie zametki
%D 2016
%P 526-536
%V 99
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a4/
%G ru
%F MZM_2016_99_4_a4
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/

[1] A. Ya. Khelemskii, “O gomologicheskoi razmernosti normirovannykh modulei nad banakhovymi algebrami”, Matem. sb., 81:3 (1970), 430–444 | MR | Zbl

[2] G. Wittstock, “Injectivity of the module tensor product of semi-Ruan modules”, J. Operator Theory, 65:1 (2011), 87–113 | MR | Zbl

[3] E. G. Effros, N. Ozawa, Z.-J. Ruan, “On injectivity and nuclearity for operator spaces”, Duke Math. J., 110:3 (2001), 489–521 | DOI | MR | Zbl

[4] B. Forrest, “Projective operator spaces, almost periodicity and completely complemented ideals in the Fourier algebra”, Rocky Mountain J. Math., 41:1 (2011), 155–176 | DOI | MR | Zbl

[5] A. Ya. Khelemskii, “Metricheskaya svoboda i proektivnost dlya klassicheskikh i kvantovykh normirovannykh modulei”, Matem. sb., 204:7 (2013), 127–158 | DOI | MR | Zbl

[6] A. W. M. Graven, “Injective and projective Banach modules”, Indag. Math., 82:3 (1979), 253–272 | DOI | MR | Zbl

[7] S. M. Shteiner, “Topologicheskaya svoboda dlya klassicheskikh i kvantovykh normirovannykh modulei”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1 (110), 49–57 | Zbl

[8] A. Ya. Khelemskii, Gomologiya v banakhovykh i topologicheskikh algebrakh, Izd-vo Mosk. un-ta, M., 1986 | MR | Zbl

[9] H. G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monogr. (N.S.), 24, Clarendon Press, New York, 2000 | MR | Zbl

[10] A. Ya. Khelemskii, Banakhovy i polinormirovannye algebry: obschaya teoriya, predstavleniya, gomologii, Nauka, M., 1989 | MR | Zbl

[11] D. P. Blecher, T. Kania, “Finite generation in $C^*$-algebras and Hilbert $C^*$-modules”, Studia Math., 224:2 (2014), 143–151 | DOI | MR | Zbl

[12] A. Ya. Khelemskii, Lektsii po funktsionalnomu analizu, MTsNMO, M., 2015

[13] D. Cushing, Z. A. Lykova, “Projectivity of Banach and $C^*$-algebras of continuous fields”, Q. J. Math., 64:2 (2013), 341–371 | DOI | MR | Zbl