Elements in a commutative Banach algebra determining the norm topology
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- by A. R. Villena PDF
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Abstract:
For an element $a$ of a commutative complex Banach algebra $(A,\|\cdot \|)$ we investigate the following property: every complete norm $|\cdot |$ on $A$ making the multiplication by $a$ from $(A,|\cdot |)$ to itself continuous is equivalent to $\|\cdot \|$.References
- Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR 0423029, DOI 10.1007/978-3-642-65669-9
- H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), no. 2, 129–183. MR 500923, DOI 10.1112/blms/10.2.129
- John M. Bachar, Philip C. Curtis Jr., H. Garth Dales, and Marc P. Thomas (eds.), Radical Banach algebras and automatic continuity, Lecture Notes in Mathematics, vol. 975, Springer-Verlag, Berlin-New York, 1983. MR 697577
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- L. E. Dickson, All integers except $23$ and $239$ are sums of eight cubes, Bull. Amer. Math. Soc. 45 (1939), 588–591. MR 28, DOI 10.1090/S0002-9904-1939-07041-9
- Allan M. Sinclair, Automatic continuity of linear operators, London Mathematical Society Lecture Note Series, No. 21, Cambridge University Press, Cambridge-New York-Melbourne, 1976. MR 0487371, DOI 10.1017/CBO9780511662355
- A. R. Villena, Operators determining the complete norm topology of $C(K)$, Studia Math. 124 (1997), no. 2, 155–160. MR 1447621, DOI 10.4064/sm-124-2-155-160
Additional Information
- A. R. Villena
- Affiliation: Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
- Email: avillena@ugr.es
- Received by editor(s): May 19, 1999
- Received by editor(s) in revised form: June 28, 1999
- Published electronically: November 8, 2000
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1057-1064
- MSC (2000): Primary 43A20, 46E25, 46J10, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-00-05659-8
- MathSciNet review: 1709768