Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-06T16:17:25.364Z Has data issue: false hasContentIssue false
  • English
  • Français

Banach algebras of topologically bounded index

Published online by Cambridge University Press:  17 April 2009

J.J. Green
J.J. Green
Affiliation:
Department of Pure MathematicsThe University of SheffieldSheffieldUnited Kingdom
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider normed and Banach algebras satisfying a condition topologically analogous to bounded index for rings. We investigate stability properties, prove a topological version of a theorem of Jacobson, and find in many cases co-incidence with well-known finiteness properties.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 51 - 62
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Aristov, O.Yu., ‘Characterization of strict C*-algebras’, Studia Math. 112 (1994), 51–58.CrossRefGoogle Scholar
[2]Bonsall, F.F. and Duncan, J., Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebeite 80 (Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
[3]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups Volume I, Mathematical surveys 7 (American Mathematical Society, Providence, RI, 1961).CrossRefGoogle Scholar
[4]Dixon, P.G., ‘Topologically nilpotent Banach algebras and factorisation’, Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 329–341.Google Scholar
[5]Dixon, P.G. and Müller, V., ‘A note on topologically nilpotent Banach algebras’, Studia Math. 102 (1992), 269–275.CrossRefGoogle Scholar
[6]Jacobson, N., ‘Some remarks on one-sided inverses’, Proc. Amer. Math. Soc. 1 (1950), 352–355.CrossRefGoogle Scholar
[7]Johnson, B. E., ‘Near inclusions for subhomogeneous C*-algebras’, Proc. London Math. Soc. 68 (1994), 399–422.CrossRefGoogle Scholar
[8]Kadison, R.V. and Ringrose, J.R., Fundamentals of the theory of operator algebras, Volume II (Academic Press, Orlando, 1989).Google Scholar
[9]Klein, A.A., ‘Rings of bounded index’, Comm. Alg. 12 (1984), 9–21.CrossRefGoogle Scholar
[10]Krupnik, N.Ya., Banach algebras with symbol and singular integral operators. Operator theory advances and applications 26 (Birkhäuser Verlag Basel, Boston, 1987).CrossRefGoogle Scholar
[11]Miziolek, J.K., Müldner, T. and Rek, A., ‘On topologically nilpotent algebras’, Studia Math. 43 (1972), 42–50.CrossRefGoogle Scholar
[12]Okniński, J., Semigroup algebras (Marcel Dekker, New York, 1991).Google Scholar
[13]Palmer, T. W., Banach algebras and the general theory of *-algebras: Volume I (Cambridge University Press, Cambridge, 1994).CrossRefGoogle Scholar
[14]Străatilă, S. and Zsidoo, L., Lectures in von Neumann algebras (Abacus Press, Tunbridge Wells, 1979).Google Scholar
[15]Varopoulos, N. Th., ‘Some remarks on Q-algebras’, Ann. Inst. Fourier (Grenoble) 22 (1972), 1–11.CrossRefGoogle Scholar