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M-Ideals and Function Algebras

Published online by Cambridge University Press:  20 November 2018

K. Seddighi  and
H. Zahedani
K. Seddighi
Affiliation:
Department of Mathematics and Statistics Shiraz University Shiraz Iran 71454
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Abstract

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Let C(X) be the space of all continuous complex-valued functions defined on the compact Hausdorff space X. We characterize the M-ideals in a uniform algebra A of C(X) in terms of singular measures. For a Banach function algebra B of C(X) we determine the connection between strong hulls for B and its peak sets. We also show that M(X) the space of complex regular Borel measures on X has no M-ideal.

Keywords

46J1046E15Singular measuresstrong hullM -idealBanach function algebrauniform algebra
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 123 - 128
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Alfsen, E. M. andEffros, E. G., Structure in real Banach spaces!, Ann. of Math. 96(1972), 98–173.Google Scholar
2. Behrends, E., M-structure and the Banach-Stone Theorem, Lecture Notes in Math. 736, Springer-Verlag, Berlin, 1979.Google Scholar
3. Conway, J. B., A course in functional analysis, Springer-Verlag, New York, 1985.Google Scholar
4. Curtis, P. C., Jr. and A. Figa-Talamanca, Factorization theorems for Banach algebras, Proc. Int. Symp. Function algebras, Scott-Foresman (1966), 169-185.Google Scholar
5. Gamelin, T. W., Uniform algebras, Prentice-Hall, Englewood Cliffs, N. J., 1969.Google Scholar
6. Harmand, P. and T.S.S.R.Rao, K., An intersection property of balls and relations with M-ideals, Mat. Zeit. 197(1988), 277–290.Google Scholar
7. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis II, Springer-Verlag, Berlin, 1963.Google Scholar
8. Hirsberg, B., M-ideals in complex function spaces and algebras, Israel J. Math. 12(1972), 133–146.Google Scholar
9. Rickart, C. E., General theory of Banach algebras, Van-Nostrand, 1960.Google Scholar
10. Smith, R. R. and Ward, J. D., Application of convexity and M-ideal theory to quotient Banach algebras, Quart. J. of Math. Oxford (2), 30(1979), 365–384.Google Scholar