# IJPAM: Volume 85, No. 3 (2013)

**ON CERTAIN p-ADIC BANACH LIMITS OF**

p-ADIC TRIANGULAR MATRIX ALGEBRAS

p-ADIC TRIANGULAR MATRIX ALGEBRAS

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**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2013

**Volume:**85

**Issue:**3