Geodesic
Algebraic ideals of semiprime Banach algebras
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 359-363

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

If A is a semiprime Banach algebra, soc A, rad A the socle and radical of A, then Soc A ∩ rad A = (0). This elementary result enables us to prove some results concerning algebraic ideal and algebraic elements modulo the socle of A. We also deduce several conditions for A equivalent to the condition dim A <+∞. 
Giotopoulos, S.; Roumeliotis, M. Algebraic ideals of semiprime Banach algebras. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 359-363. doi: 10.1017/S0017089500008429
@article{10_1017_S0017089500008429,
     author = {Giotopoulos, S. and Roumeliotis, M.},
     title = {Algebraic ideals of semiprime {Banach} algebras},
     journal = {Glasgow mathematical journal},
     pages = {359--363},
     year = {1991},
     volume = {33},
     number = {3},
     doi = {10.1017/S0017089500008429},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008429/}
}
TY  - JOUR
AU  - Giotopoulos, S.
AU  - Roumeliotis, M.
TI  - Algebraic ideals of semiprime Banach algebras
JO  - Glasgow mathematical journal
PY  - 1991
SP  - 359
EP  - 363
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008429/
DO  - 10.1017/S0017089500008429
ID  - 10_1017_S0017089500008429
ER  - 
%0 Journal Article
%A Giotopoulos, S.
%A Roumeliotis, M.
%T Algebraic ideals of semiprime Banach algebras
%J Glasgow mathematical journal
%D 1991
%P 359-363
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008429/
%R 10.1017/S0017089500008429
%F 10_1017_S0017089500008429

[1] 1.Alexander, J. C., Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1–18. Google Scholar | DOI

[2] 2.Akemann, C. and Pedersen, G. K., Ideal perturbations in C*-algebras, Math. Scand. 41 (1977), 117–139. Google Scholar | DOI

[3] 3.Allan, G. R., Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329–340. Google Scholar | DOI

[4] 4.Barnes, B., On the existence of minimal ideals in a Banach algebra, Trans. Amer. Math.Soc. 133 (1968), 511–517. Google Scholar | DOI

[5] 5.Barnes, B., Algebraic elements of a Banach algebra modulo an ideal, Pacific J. Math. 117 (1985), 219–231. Google Scholar | DOI

[6] 6.Barnes, B., Murphy, G., Smyth, M. and West, T., Riesz and Fredholm theory in Banach algebras, Research Notes in Mathematics 67 (Pitman, London, 1982)). Google Scholar

[7] 7.Bonsall, F. and Duncan, J., Complete normed algebras, (Springer-Verlag, 1973). Google Scholar | DOI

[8] 8.Leoni Dalla, S.Giotopoulos and Nelli Katseli, The socle and finite dimensionality of a semiprime Banach algebra, Studia Math.. 92 (1989), 201–204. Google Scholar | DOI

[9] 9.Dixon, P. G., Semiprime Banach algebras, J. London Math. Soc. (2) 6 (1973), 676–678. Google Scholar | DOI

[10] 10.Dixon, P. G., Locally finite Banach algebras, J. London Math. Soc. (2) 8 (1974), 325–328. Google Scholar | DOI

[11] 11.Kaplansky, I., Ring isomorphisms of Banach algebras, Canad. J. Math. 6 (1954), 374–381. Google Scholar | DOI

[12] 12.Smyth, M. R. F., Riesz theory in Banach algebras, Math. Z. 145 (1975), 145–155. Google Scholar | DOI

[13] 13.Tullo, A. W., Conditions on Banach algebras which imply finite dimensionality. Proc. Edinburgh Math. Soc. (2) 20 (1976), 1–5. Google Scholar | DOI

Cité par Sources :