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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, $\~{B}$ ).



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1. Bierstedt, K. D., Introduction to topological tensor products, Lecture Notes, Mathematical Institute, University of Paderborn (Paderborn, 2007).
2. Conway, J. H., A course in functional analysis (Springer, New York, 1985).
3. Dales, H. G., Banach algebras and automatic continuity, LMS monographs, vol. 24 (Clarendon Press, Oxford, 2000).
4. Font, Juan J., Automatic continuity of certain isomorphisms between regular Banach function algebras, Glasgow Math. J. 39 (1997), 333343.
5. Hausner, A., Ideals in a certain Banach algebra, Proc. Amer. Math. Soc. 8 (2) (1957), 246249.
6. Kaniuth, E., A course in commutative banach algebras (Springer, New York, 2009).
7. Nikou, A. and O'Farrell, A. G., Banach algebras of vector-valued functions, Glasgow Math. J. 56 (2014), 419426.
8. Ryan, R., Introduction to tensor products of banach spaces (Springer, New York, 2002).
9. Tomiyama, J., Tensor products of commutative Banach algebras, Tohoku Math. J. 12 (1960), 147154.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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