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The symmetric algebra of quotients of an ultraprime Banach algebra

Part of: Special classes of linear operators Selfadjoint operator algebras Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Martin Mathieu
Martin Mathieu
Affiliation:
Mathematisches Institut Universität TübingenAuf der Morgenstelle 10 D-7400 Tübingen Federal Republic of, Germany
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Abstract

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We present a symmetric version of a normed algebra of quotients for each ultraprime normed algebra. In addition, a C*-a1gebra of quotients of an arbitrary C*-a1gebra is introduced.

MSC classification

Secondary: 46H20: Structure, classification of topological algebras 46L05: General theory of $C^*$-algebras 47B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 75 - 87
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Amitsur, S. A., ‘On rings of quotients’, Sympos. Math. 8 (1972), 149–164.Google Scholar
[2]Ara, P., ‘The extended centroid of C *-algebras’, Arch. Math., 54 (1990), 358–364.CrossRefGoogle Scholar
[3]Barnes, B. A., Murphy, G. J., Smyth, M. R. F. and West, T. T., Riesz and Fredholm Theory in Banach algebras, (Pitman Research Notes in Math. 67, Boston, Mass., 1982).Google Scholar
[4]Garcia, M. Cabrera and Palacios, A. Rodriguez, ‘Extended centroid and central closure of semiprime normed algebras. A first approach’, Comm. Algebra, to appear.Google Scholar
[5]Johnson, B. E., ‘An introduction to the theory of centralizers’, Proc. London Math. Soc. 14 (1964), 299–320.CrossRefGoogle Scholar
[6]Martindale, W. S., ‘Prime rings satisfying a generalized polynomial identity’, J. Algebra 12 (1969), 576–584.CrossRefGoogle Scholar
[7]Mathieu, M., ‘Elementary operators on prime C *-algebras, I’, Math. Ann. 284 (1989), 223–244.CrossRefGoogle Scholar
[8]Mathieu, M., ‘Elementary operators on prime C *-algebras, II’, Glasgow Math. J. 30 (1988), 275–284.CrossRefGoogle Scholar
[9]Mathieu, M., Rings of quotients of ultraprime Banach algebras. With applications to elementary operators, (Proc. Centre Math. Anal. Austral. Nat. Univ. 21, 1989, 297–317).Google Scholar
[10]Passman, D. S., Group rings, crossed products and Galois theory, (CBMS Series no. 64, Amer. Math. Soc., Providence, R.I., 1986).Google Scholar
[11]Passman, D. S., ‘Computing the symmetric rings of quotients’, J. Algebra 105 (1987), 207–235.CrossRefGoogle Scholar
[12]Pedersen, G. K., C*-algebras and their automorphism groups, (Academic Press, London 1979).Google Scholar
[13]Pym, J. S., ‘Inductive and projective limits of normed spaces’, Glasgow Math. J. 9 (1968), 103–105.CrossRefGoogle Scholar
[14]Semadeni, Z., Banach spaces of continuous functions, (Polish Scientific Publishers, Warsaw, 1971).Google Scholar
[15]Willis, G., private communication. See also: Ultraprime group algebras, (Proc. Centre Math. Anal. Austral. Nat. Univ. 21, 1989, pp. 345–349).Google Scholar