Opuscula Math. 34, no. 1 (), 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.
Cite this article as:
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

Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.