Geodesic
Goursat's Lemma in the Context of Banach Algebras
Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 61-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The classical Goursat lemma is extended to classes of differentiable mappings of domains of real Banach spaces to algebras of linear operators acting on these spaces. We clarify the modification of the form and content of this lemma in dependence on the choice of the original object. The case in which the original space is a Banach algebra and Fréchet derivatives are operators of multiplication by elements of this algebra is considered separately.
Mots-clés : Goursat lemma, Fréchet derivative.
Keywords: Banach space, Banach algebra 
@article{MZM_2015_98_1_a4,
     author = {E. A. Gorin},
     title = {Goursat's {Lemma} in the {Context} of {Banach} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {61--75},
     year = {2015},
     volume = {98},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a4/}
}
TY  - JOUR
AU  - E. A. Gorin
TI  - Goursat's Lemma in the Context of Banach Algebras
JO  - Matematičeskie zametki
PY  - 2015
SP  - 61
EP  - 75
VL  - 98
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a4/
LA  - ru
ID  - MZM_2015_98_1_a4
ER  - 
%0 Journal Article
%A E. A. Gorin
%T Goursat's Lemma in the Context of Banach Algebras
%J Matematičeskie zametki
%D 2015
%P 61-75
%V 98
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a4/
%G ru
%F MZM_2015_98_1_a4
E. A. Gorin. Goursat's Lemma in the Context of Banach Algebras. Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 61-75. http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a4/

[1] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1962 | MR | Zbl

[2] N. Burbaki, Differentsiruemye i analiticheskie mngoobraziya. Svodka rezultatov, Mir, M., 1975 | MR

[3] E. A. Gorin, K. Sanches Fernandes, “O transtsendentnykh uravneniyakh v kommutativnykh banakhovykh algebrakh”, Funkts. analiz i ego pril., 11:1 (1977), 63–64 | MR | Zbl

[4] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972 | MR | Zbl

[5] L. Khermander, Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR | Zbl

[6] G. Grauert, R. Remmert, Teoriya prostranstv Shteina, Nauka, M., 1989 | MR

[7] E. A. Gorin, V. Ya. Lin, “Algebraicheskie uravneniya s nepreryvnymi koeffitsientami i nekotorye voprosy algebraicheskoi teorii kos”, Matem. sb., 78:4 (1969), 579–610 | MR | Zbl

[8] E. A. Gorin, “Funktsionalno-algebraicheskii variant teoremy Bora–van Kampena”, Matem. sb., 82:2 (1970), 260–272 | MR | Zbl

[9] J. L. Taylor, Measure Algebras, Reg. Conf. Ser. in Math., 16, Amer. Math. Soc., Providens, RI, 1973 | DOI | MR | Zbl

[10] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956 | MR | Zbl