Banach Journal of Mathematical Analysis

Bounded structures of uniformly $A$-convex algebras

Mohamed Oudadess

Full-text: Open access

Abstract

We examine the uniqueness of the bounded structure of semisimple and Mackey complete uniformly $A$-convex algebras. We also consider the particular locally $C^{\ast}$-case and the uniform one.

Article information

Source
Banach J. Math. Anal., Volume 3, Number 1 (2009), 19-27.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336419

Digital Object Identifier
doi:10.15352/bjma/1240336419

Mathematical Reviews number (MathSciNet)
MR2461741

Zentralblatt MATH identifier
1163.46035

Subjects
Primary: 46J05: General theory of commutative topological algebras
Secondary: 46K05: General theory of topological algebras with involution

Keywords
uniformly A-convex algebra bounded structure Mackey completeness locally C*-algebra uniform algebra

Citation

Oudadess, Mohamed. Bounded structures of uniformly $A$-convex algebras. Banach J. Math. Anal. 3 (2009), no. 1, 19--27. doi:10.15352/bjma/1240336419. https://projecteuclid.org/euclid.bjma/1240336419


Export citation

References

  • S.T. Bhatt and D.J. Karia, Uniqueness of the uniform norm with an application to topological algebras, Proc. Amer. Math. Soc., 116 (1992), 499–503.
  • S.T. Bhatt, Norm-Free Topological Algebra Characterizations of $C^\ast $-Algebras and Uniform Banach Algebras, Bull. Polish Acad. Sci. Math. 45 (1997), no.2, 117–121.
  • R.L. Carpenter, Uniqueness of topology for commutative semi-simple $F$-algebras, Proc. Amer. Math. Soc. 29 (1971), 113–117.
  • A.C. Cochran, R. Keown and C.R. Williams, On a class of topological algebras, Pacific J. Math. 34 (1970), 17–25.
  • A.C. Cochran, Representation of $A$-convex algebras, Proc. Amer. Math. Soc. 41 (1973), 473–479.
  • H.V. Dedania, A seminorm with square property is automatically submultipplicative, Proc. Indian Acad. Sci. (Math. Sci.) 108 (1998), 51–53.
  • A. El Kinani, M. Oudadess, Locally boundedly $A$-$p$-convex algebras, Math. Nach. 266 (2004), 27-33.
  • M. Fragoulopoulou, Topological Algebras with Involution, North-Holland, Math. Studies 200, 2005.
  • A. Mallios, Topological algebras: Selected topics, North-Holland, Amserdam, 1986.
  • E.A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc. 1952, 1952, no. 11, 79 pp.
  • M. Oudadess, Théorèmes de structures et propriét és fondamentales des algèbres localement uniformémnt $A$ -convexes, C. R. Acad. Sci. Paris, Sér. I Math. 296 (1983), 851–853.
  • M. Oudadess, Une norme d'algèbre de Banach dans les alg èbres uniformément $A$-convexes, Africa Math., 9 (1987), 15–22.
  • M. Oudadess, Théorème du type Gelfand-Naimark dans les algèbres uniformément $A$-convexes, Ann. Sc. Math. Québec, 9 (1985), no. 1, 73–82.
  • M. Oudadess, Discontinuity of the product in multiplier algebras, Publications Mathématiques 34 (1990), 397–401.
  • M. Oudadess, Functional bounddness of some $M$-complete $m$ -convex algebras, Bull. Greek Math. Soc. 39 (1997), 17–20.
  • Z. Sebestyén, Every $C^\ast $-seminorm is automatically submultiplicative, Period. Math. Hungar. 10 (1979), 1–8.