IJPAM: Volume 85, No. 3 (2013)

ON CERTAIN p-ADIC BANACH LIMITS OF
p-ADIC TRIANGULAR MATRIX ALGEBRAS

R.L. Baker
University of Iowa
Iowa City, Iowa 52242, USA


Abstract. In this paper we investigate the class of p-adic triangular UHF (TUHF) Banach algebras. A p-adic TUHF Banach algebra is any unital p-adic Banach algebra \cal T of the form {\cal T}=\overline{\bigcup{\cal T}_n}, where ({\cal T}_n) is an increasing sequence of p-adic Banach subalgebras of \cal T such that each {\cal T}_n contains the identity of \cal T and is isomorphic as an \Omega_p-algebra to T_{p_n}(\Omega_p) for some p_n, where T_{p_n}(\Omega_p) is the algebra of upper triangular p_n\times p_n matrices over the p-adic field \Omega_p. The main result is that the supernatural number associated to a p-adic TUHF Banach algebra is an invariant of the algebra, provided that the algebra satisfies certain local dimensionality conditions.

Received: March 15, 2011

AMS Subject Classification: 12J25, 12J99, 46L99, 46S10

Key Words and Phrases: p-adic Banach algebras, p-adic Banach limits, p-adic UHF algebras, p-adic Triangular UHF algebras

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DOI: 10.12732/ijpam.v85i3.1 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 3