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Topological modules of continuous homomorphisms. (English) Zbl 1152.46039
L’auteur complète certaines propriétés relatives aux homomorphismes continus entre modules topologiques et dues à divers auteurs. Le résultat le plus intéressant est le suivant: $A$ est une algèbre topologique, $X$ un $A$-module topologique séparé avec une multiplication de module telle que pour chaque voisinage $G$ de l’origine dans $X$ et chaque partie bornée $D$ de $A$ il existe un voisinage $H$ de l’origine dans $X$ vérifiant $D\cdot H\subseteq G$. On suppose que $A$ possède une unité approchée $\{e_\lambda\}$; la partie essentielle $X_e$ de $X$ est formée des éléments $x$ de $X$ pour lesquels $\{e_\lambda\cdot x\}$ converge vers $x$ pour la topologie $\tau$ de $X$ supposée complète. Finalement $[\Hom_A(A, X_e)]_e$ muni de la topologie de la convergence bornée est isomorphe à $X_e$ pour la topologie $\tau$.

MSC:
46H25Normed modules and Banach modules, topological modules
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References:
[1] Abel, M.: Topological bimodule-algebras, Proc. 3rd internat. Conf. topological algebras appl., 25-42 (2004) · Zbl 1077.46045 · http://herkules.oulu.fi/isbn9514272498/
[2] Ansari-Piri, E.: A class of factorizable topological algebras, Proc. Edinburgh math. Soc. 33, 53-59 (1990) · Zbl 0699.46027 · doi:10.1017/S001309150002887X
[3] Arnautov, V. I.; Glavatsky, S. T.; Mikhalev, A. V.: Introduction to the theory of topological rings and modules, (1996) · Zbl 0842.16001
[4] Buck, R. C.: Bounded continuous functions on a locally compact space, Michigan math. J. 5, 95-104 (1958) · Zbl 0087.31502 · doi:10.1307/mmj/1028998054
[5] Busby, R. C.: Double centralizers and extension of C$\ast $-algebras, Trans. amer. Math. soc. 132, 79-99 (1968) · Zbl 0165.15501 · doi:10.2307/1994883
[6] Doran, R. S.; Wichmann, J.: Approximate identities and factorization in Banach modules, Lecture notes in math. 768 (1979) · Zbl 0418.46039
[7] Edwards, R. E.: Functional analysis, theory and application, (1965) · Zbl 0182.16101
[8] Haro, J. C. C.; Lai, H. C.: Multipliers in continuous vector-valued function spaces, Bull. austral. Math. soc. 46, 199-204 (1992) · Zbl 0761.43003 · doi:10.1017/S0004972700011837
[9] Husain, T.: The open mapping and closed graph theorems in topological vector spaces, Oxford math. Monogr. (1965) · Zbl 0124.06301
[10] Husain, T.: Multipliers of topological algebras, Dissertationes math. 285, 1-36 (1989) · Zbl 0676.46038
[11] Iyahen, S. O.: On certain classes of linear topological spaces, Proc. London math. Soc. (3) 18, 285-307 (1968) · Zbl 0165.14203 · doi:10.1112/plms/s3-18.2.285
[12] Johnson, B. E.: An introduction to the theory of centralizers, Proc. London math. Soc. 14, 299-320 (1964) · Zbl 0143.36102 · doi:10.1112/plms/s3-14.2.299
[13] Johnson, B. E.: Continuity of centralizers on Banach algebras, J. London math. Soc. 41, 639-640 (1966) · Zbl 0143.36103 · doi:10.1112/jlms/s1-41.1.639
[14] Khan, L. A.: The strict topology on topological modules, Contemp. math. 435, 253-263 (2007) · Zbl 1148.46306
[15] Khan, L. A.; Mohammad, N.; Thaheem, A. B.: Double multipliers on topological algebras, Int. J. Math. math. Sci. 22, 629-636 (1999) · Zbl 1007.46042 · doi:10.1155/S0161171299226294
[16] Mallios, A.: Topological algebras --- selected topics, North-holland math. Stud. 124 (1986) · Zbl 0597.46046
[17] Oztop, S.: Multipliers of Banach valued weighted function spaces, Int. J. Math. math. Sci. 24, No. 8, 511-517 (2000) · Zbl 0968.43004 · doi:10.1155/S0161171200004361
[18] Phillips, N. C.: Inverse limits of C$\ast $-algebras, J. operator theory 19, 159-195 (1988) · Zbl 0662.46063
[19] Jr., D. P. Pombo: On modules of continuous linear mappings, Int. J. Math. math. Sci. 21, 197-198 (1998) · Zbl 0903.46047 · doi:10.1155/S016117129800026X
[20] Quek, T. S.: Multipliers of certain vector valued function spaces, J. math. Anal. appl. 115, 406-421 (1986) · Zbl 0604.46041 · doi:10.1016/0022-247X(86)90004-1
[21] Rieffel, M. A.: Induced Banach representations of Banach algebras and locally compact groups, J. funct. Anal. 1, 443-491 (1967) · Zbl 0181.41303 · doi:10.1016/0022-1236(67)90012-2
[22] Rieffel, M. A.: Multipliers and tensor products on lp-spaces of locally compact groups, Studia math. 33, 71-82 (1969) · Zbl 0177.41702
[23] Rieffel, M. A.: On the continuity of certain intertwining operators, centralizers, and positive linear functionals, Proc. amer. Math. soc. 20, 455-457 (1969) · Zbl 0177.41301 · doi:10.2307/2035676
[24] Ruess, W.: On the locally convex structure of strict topologies, Math. Z. 153, 179-192 (1977) · Zbl 0361.46002 · doi:10.1007/BF01179791
[25] Sentilles, F. D.; Taylor, D. C.: Factorization in Banach algebras and the general strict topology, Trans. amer. Math. soc. 142, 141-152 (1969) · Zbl 0185.21103 · doi:10.2307/1995349
[26] Shantha, K. V.: The general strict topology in locally convex modules over locally convex algebras I, Ital. J. Pure appl. Math. 16, 211-226 (2004) · Zbl 1172.46303
[27] Summers, M. K.: Factorization in Fréchet modules, J. London math. Soc. (2) 5, 243-248 (1972) · Zbl 0239.46043 · doi:10.1112/jlms/s2-5.2.243
[28] Tewari, U.; Dutta, M.; Vaidya, D. P.: Multipliers of group algebras of vector valued functions, Proc. amer. Math. soc. 81, 223-229 (1981) · Zbl 0458.43005 · doi:10.2307/2044199
[29] Tomiuk, B. J.: Multipliers on Banach algebras, Studia math. 54, 267-283 (1976) · Zbl 0319.46033
[30] Waelbroeck, L.: Topological vector spaces and algebras, Lecture notes in math. 230 (1971) · Zbl 0225.46001
[31] Wang, J. K.: Multipliers of commutative Banach algebras, Pacific J. Math. 11, 1131-1149 (1961) · Zbl 0127.33302
[32] Warner, S.: Topological fields, North-holland math. Stud. 178 (1989)
[33] &zdot, W.; Elazko: Selected topics in topological algebras, Lect. notes ser. 31 (1971)