TY  - JOUR
ID  - Cho2014
LB  - Cho2014
AU  - Cho, Ilwoo
TI  - p-adic Banach space operators and adelic Banach space operators
ST  - p-adic Banach space operators and adelic Banach space operators
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 1
SP  - 29
EP  - 65
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.1.29
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.1.29
AB  - 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.
KW  - prime fields
KW  - \(p\)-adic number fields
KW  - adele ring
KW  - \(p\)-adic Banach spaces
KW  - adelic Banach space
KW  - \(p\)-adic operators
KW  - adelic operators
SN  - 1232-9274
ER  -