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The Mahler basis and other bases. (Base de Mahler et autres.) (French) Zbl 0999.12014

This is an exposition of results of L. Van Hamme [\(p\)-adic functional analysis, Laredo, 1990, 75–88 (1992; Zbl 0773.47039)]. Moreover the author gives the results in a historical context and adds some further results. The aim is to find orthonormal bases for the Banach space of continuous functions from \({\mathbb Z}_p\) to \(K\) (a complete nonarchimedean valued field). The norm is the supremum norm.

MSC:

12J25 Non-Archimedean valued fields
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory

Citations:

Zbl 0773.47039
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