Opuscula Math. 34, no. 1 (2014), 29-65
http://dx.doi.org/10.7494/OpMath.2014.34.1.29
Opuscula Mathematica
p-adic Banach space operators and adelic Banach space operators
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.
Mathematics Subject Classification: 05E15, 11G15, 11R47, 46L10, 47L30, 47L55.
- Ilwoo Cho
- St. Ambrose University, Department of Mathematics, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
- Received: 2013-04-11.
- Revised: 2013-06-21.
- Accepted: 2013-07-22.
