Proceedings of the Edinburgh Mathematical Society (Series 2)
- Proceedings of the Edinburgh Mathematical Society (Series 2) / Volume 21 / Issue 02 / September 1978, pp 159-166
- Copyright © Edinburgh Mathematical Society 1978
- DOI: http://dx.doi.org/10.1017/S0013091500016126 (About DOI), Published online: 20 January 2009
Research Article
On central traces and groups of symmetries of order unit Banach spaces
Cho-Ho Chua1*
a1 University of Benin, Benin City, Nigeria
A central trace on an order-unit Banach space A(K) is a centre-valued module homomorphism invariant under the group of symmetries of A(K).
The concept of central traces has been crucial in the theory of types for convex sets established in (4), (5). In von Neumann algebras, they are precisely the canonical centre-valued traces and their existence hinges on a fundamental theorem (Dixmier's approximation process) in von Neumann algebras. On the other hand, the existence of central traces in finite dimensional spaces is an easy consequence of Ryll-Nardzewski's fixed point theorem (5).
(Received March 03 1977)
Footnotes
* Work done at the University of Tripoli.
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