This article is cited in 2 papers

The Notion of a Trace on Order-Unit Spaces and the Space of Integrable Elements

M. A. Berdikulov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: Some definitions are given of the notion of a trace on an order-unit space, interrelations of the definitions are studied, and the space of integrable elements is constructed. Using one of the definitions of a trace, we prove that the predual of an order-unit space is isometrically isomorphic to the space of trace-integrable elements.

Key words: order unity, order-unit space, base-norm space, $P$-projections, projection units, trace, generalized spin-factor.

UDC: 517.98

Received: 21.04.2004

 English version: Siberian Advances in Mathematics, 2006, 16:2, 34–42

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