Opuscula Math. 34, no. 1 (2014), 29-65
http://dx.doi.org/10.7494/OpMath.2014.34.1.29

Opuscula Mathematica

Ilwoo Cho

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.

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• Ilwoo Cho
• St. Ambrose University, Department of Mathematics, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
• Revised: 2013-06-21.
• Accepted: 2013-07-22.

Ilwoo Cho, p-adic Banach space operators and adelic Banach space operators, Opuscula Math. 34, no. 1 (2014), 29-65, http://dx.doi.org/10.7494/OpMath.2014.34.1.29

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