Montel subspaces of Fréchet spaces of Moscatelli type
Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 345-350

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we show that every complemented Montel subspace F of a Fréchet space E of Moscatelli type is isomorphic to ω or is finite–dimensional; the last case always occurs when E has a continuous norm. To do this, we first study the topology induced by E on its Montel subspaces, extending a result on Fr6chet-Montel spaces of Moscatelli type in [4].We recall that the Fréchet spaces of Moscatelli type were introduced and studied by J. Bonet and S. Dierolf in [4]; the general idea behind the construction of such spaces was due to V. B. Moscatelli [7].
Albanese, Angela A. Montel subspaces of Fréchet spaces of Moscatelli type. Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 345-350. doi: 10.1017/S0017089500032262
@article{10_1017_S0017089500032262,
     author = {Albanese, Angela A.},
     title = {Montel subspaces of {Fr\'echet} spaces of {Moscatelli} type},
     journal = {Glasgow mathematical journal},
     pages = {345--350},
     year = {1997},
     volume = {39},
     number = {3},
     doi = {10.1017/S0017089500032262},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500032262/}
}
TY  - JOUR
AU  - Albanese, Angela A.
TI  - Montel subspaces of Fréchet spaces of Moscatelli type
JO  - Glasgow mathematical journal
PY  - 1997
SP  - 345
EP  - 350
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500032262/
DO  - 10.1017/S0017089500032262
ID  - 10_1017_S0017089500032262
ER  - 
%0 Journal Article
%A Albanese, Angela A.
%T Montel subspaces of Fréchet spaces of Moscatelli type
%J Glasgow mathematical journal
%D 1997
%P 345-350
%V 39
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500032262/
%R 10.1017/S0017089500032262
%F 10_1017_S0017089500032262

[1] 1.Adams, R. A., Sobolev spaces (Academic Press, London 1970). Google Scholar

[2] 2.Albanese, A. A., Metafune, G. and Moscatelli, V. B., Representations of the spaces Cm(Ω)⋂Hk.p(Ω), Math. Proc. Camb. Phil. Soc., 120 (1996), 489–498. Google Scholar | DOI

[3] 3.Albanese, A. A., Metafune, G. and Moscatelli, V. B., Representations of the spaces Cm(RN)⋂Hk.p(RN), in Proceedings of the First Workshop of Functional Analysis at Trier University, (Walter de Gruyter and Co., 1996), 11–20. Google Scholar

[4] 4.Bonet, J., Dierolf, S., Frechet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (suppl.) (1989), 77–92. Google Scholar

[5] 5.Jarchow, H., Locally convex spaces (Teubner, Stuttgart, 1981). Google Scholar

[6] 6.Metafune, G. and Moscatelli, V. B., Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. 153 (4) (1988), 175–190. Google Scholar

[7] 7.Moscatelli, V. B., Fréchet spaces without continuous norms and without basis, Bull. London Math. Soc. 12 (1980), 63–66. Google Scholar

[8] 8.Carreras, P. Pérez and Bonet, J., Barrelled locally convex spaces (North Holland Math. Studies 131, 1987). Google Scholar | DOI

Cité par Sources :