Inductive limits of normed algebras and $m$-convex structures
HTML articles powered by AMS MathViewer
- by M. Oudadess PDF
- Proc. Amer. Math. Soc. 109 (1990), 399-401 Request permission
Abstract:
In this note, we give a negative answer to a question raised by A. Arosio in 1974. It concerns the multiplicativity of the inductive limit topology associated to a family of normed algebras.References
- Mohamed Akkar, Sur la théorie spectrale des opérateurs fortement bornés dans les espaces vectoriels topologiques ou bornologiques, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1805–A1808 (French). MR 320754
- Alberto Arosio, Locally convex inductive limits of normed algebras, Rend. Sem. Mat. Univ. Padova 51 (1974), 333–359 (1975). MR 377515
- A. C. Cochran, R. Keown, and C. R. Williams, On a class of topological algebras, Pacific J. Math. 34 (1970), 17–25. MR 273399, DOI 10.2140/pjm.1970.34.17
- J. Esterle, Sur la métrisabilité de certaines algèbres d’opérateurs, Rev. Roumaine Math. Pures Appl. 24 (1979), no. 8, 1157–1164 (French). MR 551965
- A. Guichardet, Leçons sur certaines algèbres topologiques: Algèbres de von Neumann; Algèbres topologiques et fonctions holomorphes; Algèbres de Banach commutatives, Gordon & Breach, Paris-London-New York; distributed by Dunod Éditeur, Paris, 1967 (French). MR 0232210
- Ernest A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952), 79. MR 51444 C. Nacir, Limites inductives bornologiques convexes et topologiques... , Thèse de 3ème Cycle, E. N. S. de Rabat, 1986.
- Mohammed Raouyane, Algèbres pseudo-Banach normalisées, Bull. Soc. Math. Belg. Sér. B 38 (1986), no. 1, 39–45 (French). MR 871302
- Seth Warner, Inductive limits of normed algebras, Trans. Amer. Math. Soc. 82 (1956), 190–216. MR 79226, DOI 10.1090/S0002-9947-1956-0079226-3
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 399-401
- MSC: Primary 46H99; Secondary 46A12
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000166-2
- MathSciNet review: 1000166