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arXiv · 2104.06329

Strongly zero product determined Banach algebras

J. Alaminos·J. Extremera·M. L. C. Godoy·A. R. Villena
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Abstract

$C^*$-algebras, group algebras, and the algebra $\mathcal{A}(X)$ of approximable operators on a Banach space $X$ having the bounded approximation property are known to be zero product determined. We are interested in giving a quantitative estimate of this property by finding, for each Banach algebra $A$ of the above classes, a constant $\alpha$ with the property that for every continuous bilinear functional $\varphi\colon A \times A\to\mathbb{C}$ there exists a continuous linear functional $\xi$ on $A$ such that \[ \sup_{\Vert a\Vert=\Vert b\Vert=1}\vert\varphi(a,b)-\xi(ab)\vert\le \alpha\sup_{\mathclap{\substack{\Vert a\Vert=\Vert b\Vert=1, \\ ab=0}}}\vert\varphi(a,b)\vert. \]

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BibTeXRIS

J. Alaminos, J. Extremera, M. L. C. Godoy, A. R. Villena. 2021-04-13. Strongly zero product determined Banach algebras. https://arxiv.org/abs/2104.06329

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