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BANACH ALGEBRAS OF VECTOR-VALUED FUNCTIONS

Published online by Cambridge University Press:  13 August 2013

AZADEH NIKOU  and
ANTHONY G. O'FARRELL
AZADEH NIKOU
Affiliation:
Department of Mathematics, Tarbiat Moallem University, 599 Taleghani Avenue, Tehran 15618, Iran e-mail: [email protected]
ANTHONY G. O'FARRELL
Affiliation:
Department of Mathematics and Statistics, NUI, Maynooth, Co. Kildare, Ireland e-mail: [email protected]
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Abstract

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We introduce the concept of an E-valued function algebra, a type of Banach algebra that consists of continuous E-valued functions on some compact Hausdorff space, where E is a Banach algebra. We present some basic results about such algebras, having to do with the Shilov boundary and the set of peak points of some commutative E-valued function algebras. We give some specific examples.

Keywords

46H99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 419 - 426
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Bagheri-Bardi, G. A., Medghalchi, A. R. and Spronk, N., Operator-valued convolution algebras, Houston J. Math. 36 (4) (2010), 1023–1036.Google Scholar
2.Browder, A., Function algebras (Benjamin, New York, NY, 1969).Google Scholar
3.Cao, H. X., Zhang, J. H. and Xu, Z. B., Characterizations and extensions of Lipschitz-α operators, Acta Math. Sin. Engl. Ser. 22 (3) (2006), 671–678.Google Scholar
4.Dales, H. G., Banach algebras and automatic continuity, LMS Monographs, 24 (Clarendon Press, Oxford, UK, 2000).Google Scholar
5.Dierolf, S., Schröder, K.-H. and Wengenroth, J., Characters on certain function algebras, Funct. Approx. Comment. Math. 26(1998) 53–58.Google Scholar
6.Gamelin, T. W., Uniform algebras (Prentice-Hall, Englewood Cliffs, NJ, 1969).Google Scholar
7.Hausner, A., Ideals in a certain Banach algebra, Proc. Amer. Math. Soc. 8 (2) (1957), 246–249.Google Scholar
8.Honary, T. G. and Mahyar, H., Approximation in Lipschitz algebras, Quaest. Math. 23 (1) (2000), 13–19.CrossRefGoogle Scholar
9.Johnson, G. P., Spaces of functions with values in a Banach algebra, Trans. Amer. Math. Soc. 92(1959) 411–429.Google Scholar
10.Kaniuth, E., A course in commutative Banach algebras, Graduate Texts in Mathematics, 246 (Springer, New York, NY, 2009).CrossRefGoogle Scholar
11.Leibowitz, G., Lectures on complex function algebras (Scott Foresman, Glenview, IL, 1970).Google Scholar
12.Sherbert, D. R.The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. AMS 111 (1964), 240–272.CrossRefGoogle Scholar
13.Stout, E. L., The theory of uniform algebras (Bogden and Quigley, Tarrytown-on-Hudson, NY, 1971).Google Scholar
14.Tomiyama, J., Tensor products of commutative Banach algebras, Tohoku Math. J. 12(1960) 147–154.Google Scholar
15.Zelazko, W., Banach algebras (Elsevier, New York, NY, 1973).Google Scholar