Geodesic
A Characterization of C*-normed Algebras via Positive Functionals
Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 114-123

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

We give a characterization of ${{C}^{*}}$ -normed algebras, among certain involutive normed ones. This is done through the existence of enough specific positive functionals. The same question is also examined in some non normed (topological) algebras.
DOI : 10.4153/CMB-2017-023-1
Mots-clés : 46H05, 46K05, C*-normed algebra, C*-algebra, (pre-)locally C*-algebra, pre-C*-bornological algebra, positive functional, locally uniformly A-convex algebra, perfect locally m-convex algebra, C*-subnormable algebra, *-subnormable algebra 
Haralampidou, Marina; Oudadess, Mohamed; Palacios, Lourdes. A Characterization of C*-normed Algebras via Positive Functionals. Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 114-123. doi: 10.4153/CMB-2017-023-1
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[1] [1] Allan, G. R., Dales, H. G., and McClure, J. P., Pseudo-Banach algebras. Studia Math. 40 (1971), 55–69. Google Scholar

[2] [2] Apostol, C., b*-algebras and their representations. J. London Math. Soc. 3 (1971), 30–38. http://dx.doi.Org/10.1112/jlms/s2-3.1.30. Google Scholar

[3] [3] Bourbaki, N., Theorie des Ensembles. Chap. 3, Hermann, Paris, 1967. Google Scholar

[4] [4] Cochran, A. C., Representation of A-convex algebras. Proc. Amer. Math. Soc. 41 (1973), 473–479. http://dx.doi.Org/10.2307/203911 6. Google Scholar

[5] [5] Cochran, A. C., Keown, R., and Williams, C. R., On a class of topological algebras. Pacific J. Math. 34 (1970), 17–25. http://dx.doi.org/10.2140/pjm.1970.34.17. Google Scholar

[6] [6] Doran, R. S., Research problems: Does there exist a Banach *-algebra without identity with no nonzero positive functionals? Amer. Math. Monthly 87 (1980), 474–475. http://dx.doi.Org/10.2307/2320257. Google Scholar

[7] [7] Fragoulopoulou, M., Topological algebras with Involution. North Holland Mathematics Studies, 200. Elsevier Science, Amsterdam, 2005. Google Scholar

[8] [8] Gorbachev, N. V., An example of a Banach âlgebra without identity and with no nonzero positive functionals. Uspekhi Mat. Nauk 38(1983), 189. Google Scholar

[9] [9] Haralampidou, M., The Krull nature oflocally C*-algebras. Function Spaces (Edwardsville IL, 2002), pp. 195-200, Contemp. Math. 328, Amer. Math. Soc, Providence, RI, 2003. http://dx.doi.org/10.1090/conm/328/05781. Google Scholar

[10] [10] Haralampidou, M., Palacios, L., and Signoret, C., Multipliers inperfect locally m-convex algebras. Banach J. Math. Anal. 9 (2015), no. 1, 137–143. http://dx.doi.org/10.15352/bjma/09-1-11. Google Scholar

[11] [11] Hogbe-Nlend, H., Les fondements de la theorie spectrale des algebres bornologiques. Bol. Soc. Brasil Mat. 3 (1972), 19–56. http://dx.doi.org/10.1007/BF02584840. Google Scholar

[12] [12] Inoue, A., Locally C*-algebras. Mem. Faculty Sei. Kyushu Univ. SerA 25 (1971), 197–235. http://dx.doi.Org/1O.22O6/kyushumfs.25.1 97. Google Scholar

[13] [13] Mallios, A., Topological algebras. Selected topics. North-Holland Mathematics Studies, 124. North-Holland, Amsterdam, 1986. Google Scholar

[14] [14] Oudadess, M., Theoreme du type Gelfand-Naimark dans les algebres uniformement A-convexes. Ann. Sc. Math. Quebec, 9 (1985), 73–82. Google Scholar

[15] [15] Oudadess, M., Une norme d'algebre de Banach dans les algebres uniformement A-convexes. Africa Math. 9 (1987), 15–22. Google Scholar

[16] [16] Oudadess, M., Bounded struetures in locally A-convex algebras. Math. Stud. (Tartu), 4. Est. Math. Soc, Tartu, 2008, pp. 80-88. Google Scholar

[17] [17] Oudadess, M., C*-bornological algebras. African Diaspora J. Math. 9 (2010), 87–95. Google Scholar

[18] [18] Oudadess, M., Subnormable A-convex algebras. De Gruyter Proceedings in Mathematics (to appear). Google Scholar

[19] [19] Phillips, N. C., Inverse limits of C*-algebras. J. Operator Tneory 19 (1988), 159–195. Google Scholar

[20] [20] Rickart, C. E., General theory of Banach algebras. D. Van Nostrand, Princeton, N.J., 1960. Google Scholar

[21] [21] Rudin, W., Functional analysis. McGraw-Hill, New York, 1973. Google Scholar

[22] [22] Varopoulos, N. Th., Sur lesformes positives d’ une algebre de Banach. C. R. Acad. Sei. Paris 258 (1964), 2465–2467. Google Scholar

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