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DITKIN CONDITIONS

Part of: Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  27 February 2017

AZADEH NIKOU  and
ANTHONY G. O'FARRELL
AZADEH NIKOU
Affiliation:
Department of Mathematics, Tarbiat Moallem University, 599 Taleghani Avenue, 15618 Tehran, Iran e-mail: a.nikou81@gmail.com
ANTHONY G. O'FARRELL
Affiliation:
Department of Mathematics and Statistics, NUI, Maynooth, Co. Kildare, Ireland e-mail: admin@maths.nuim.ie
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Abstract

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This paper is about the connection between certain Banach-algebraic properties of a commutative Banach algebra E with unit and the associated commutative Banach algebra C(X, E) of all continuous functions from a compact Hausdorff space X into E. The properties concern Ditkin's condition and bounded relative units. We show that these properties are shared by E and C(X, E). We also consider the relationship between these properties in the algebras E, B and $\~{B}$ that appear in the so-called admissible quadruples (X, E, B, $\~{B}$).

MSC classification

Primary: 46J99: None of the above, but in this section
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 153 - 163
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. Bierstedt, K. D., Introduction to topological tensor products, Lecture Notes, Mathematical Institute, University of Paderborn (Paderborn, 2007).Google Scholar
2. Conway, J. H., A course in functional analysis (Springer, New York, 1985).CrossRefGoogle Scholar
3. Dales, H. G., Banach algebras and automatic continuity, LMS monographs, vol. 24 (Clarendon Press, Oxford, 2000).Google Scholar
4. Font, Juan J., Automatic continuity of certain isomorphisms between regular Banach function algebras, Glasgow Math. J. 39 (1997), 333–343.CrossRefGoogle Scholar
5. Hausner, A., Ideals in a certain Banach algebra, Proc. Amer. Math. Soc. 8 (2) (1957), 246–249.CrossRefGoogle Scholar
6. Kaniuth, E., A course in commutative banach algebras (Springer, New York, 2009).CrossRefGoogle Scholar
7. Nikou, A. and O'Farrell, A. G., Banach algebras of vector-valued functions, Glasgow Math. J. 56 (2014), 419–426.CrossRefGoogle Scholar
8. Ryan, R., Introduction to tensor products of banach spaces (Springer, New York, 2002).CrossRefGoogle Scholar
9. Tomiyama, J., Tensor products of commutative Banach algebras, Tohoku Math. J. 12 (1960), 147–154.CrossRefGoogle Scholar