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A note on annihilator Banach algebras

Published online by Cambridge University Press:  17 April 2009

Pak-Ken Wong
Pak-Ken Wong
Affiliation:
Department of Mathematics, Seton Hall, University, South Orange, N.J. 07079, United States of America
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Abstract

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Let A be a semisimple Banach algebra with ‖ · ‖, which is a dense subalgebra of a semisimple Banach algebra B with | · | such that ‖ · ‖ majorises | · | on A. The purpose of this paper is to investigate the annihilator property between the algebras A and B.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 1 , August 1988 , pp. 77 - 81
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Barnes, B.A., ‘On the existence of minimal ideals in a Banach algebra’, Trans. Amer. Math. Soc. 133 (1968), 511–517.CrossRefGoogle Scholar
[2]Barnes, B.A., ‘Banach algebras which are ideals in a Banach algebra’, Pacific J. Math. 38 (1971), 1–7.CrossRefGoogle Scholar
[3]Johnson, D.L. and Lahr, C.D., ‘Dual A*-algebras of the first kind’, Proc. Amer. Math. Soc. 74 (1979), 311–314.Google Scholar
[4]Mackey, G.W., ‘Isomorphisms of normed linear spaces’, Ann. of Math. (2) 43 (1942), 244–260.CrossRefGoogle Scholar
[5]Ogasawara, T. and Yoshinaga, K., ‘Weakly completely continuous Banach ⋆-algebras’, J. Sci. Hiroshima Univ. Ser. A 18 (1954), 15–36.Google Scholar
[6]Rickart, C.E., General Theory of Banach Algebras, Univ. Ser. in Higher Math. (Van Nostrand, Princeton, N.J., 1960).Google Scholar
[7]Tomiuk, B.J. and Yood, B., ‘Topological algabras with dense socle’, J. Funct. Analysis 28 (1978), 254–277.CrossRefGoogle Scholar
[8]Wong, P.K., ‘Modular annihilator A*-algebras’, Pacific J. Math. 37 (1971), 825–834.CrossRefGoogle Scholar
[9]Wong, P.K., ‘On the Arens product and annihilator algebras’, Trans. Amer. Math. Soc. 30 (1971), 79–83.Google Scholar
[10]Wong, P.K., ‘On the Arens product and certain Banach algebras’, Trans. Amer. Math. Soc. 180 (1973), 437–448.CrossRefGoogle Scholar
[11]Wong, P.K., ‘The second conjugates of certain Banach algebras’, Canad. J. Math. 27 (1975), 1029–1035.CrossRefGoogle Scholar
[12]Yood, B., ‘Ideals in topological rings’, Canad. J. Math. 16 (1964), 28–45.CrossRefGoogle Scholar