IJPAM: Volume 75, No. 1 (2012)

A CERTAIN $p$-ADIC SPECTRAL THEOREM

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


Abstract. We extend a $p$-adic spectral theorem of M. M. Vishik to a certain class of $p$-adic Banach algebras. This class includes inductive limits of finite-dimensional $p$-adic Banach algebras of the form $B({\cal X})$, where $\cal X$ is a $p$-adic Banach space of the form ${\cal X}\simeq\Omega_p(J)$, $J$ being a finite nonempty set. In particular, we present a $p$-adic spectral theorem for $p$-adic UHF algebras and $p$-adic TUHF algebras (Triangular UHF Algebras).

Received: November 11, 2011

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

Key Words and Phrases: $p$-adic Banach algebras, $p$-adic UHF algebras, $p$-adic spectral theorem, $p$-adic triangular UHF algebras

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 1