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arXiv · 1512.09303

Ditkin Conditions

Azadeh Nikou·Anthony G. O'Farrell
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Abstract

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 $\tilde B$ that appear in so-called admissible quadruples $(X,E,B,\tilde B)$.

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Azadeh Nikou, Anthony G. O'Farrell. 2016-01-22. Ditkin Conditions. https://arxiv.org/abs/1512.09303

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