@Article{Cho2014,
author = "Cho, Ilwoo",
title = "p-adic Banach space operators and adelic Banach space operators",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "1",
pages = "29--65",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.1.29",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.1.29",
abstract = "In this paper, we study non-Archimedean Banach \(*\)-algebras \(\frak{M}_{p}\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\), and \(\frak{M}_{\mathbb{Q}}\) over the adele ring \(\mathbb{A}_{\mathbb{Q}}\). We call elements of \(\frak{M}_{p}\), \(p\)-adic operators, for all primes \(p\), respectively, call those of \(\frak{M}_{\mathbb{Q}}\), adelic operators. We characterize \(\frak{M}_{ \mathbb{Q}}\) in terms of \(\frak{M}_{p}\)'s. Based on such a structure theorem of \(\frak{M}_{\mathbb{Q}}\), we introduce some interesting \(p\)-adic operators and adelic operators.",
keywords = "prime fields, \(p\)-adic number fields, adele ring, \(p\)-adic Banach spaces, adelic Banach space, \(p\)-adic operators, adelic operators",
issn = "1232-9274"
}