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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: [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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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

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