Paper's Title:

The Jacobson Density Theorem for Non-Commutative Ordered Banach Algebras

Author(s):

Kelvin Muzundu

University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
Zambia.
E-mail: kmzundu@gmail.com

Abstract:

The Jacobson density theorem for general non-commutative Banach algebras states as follows: Let π be a continuous, irreducible representation of a non-commutative Banach algebra A on a Banach space X. If x₁,x₂,...,x_n are linearly independent in X and if y₁,y₂,...,y_n are in X, then there exists an a∈ A such that π(a)x_i=y_i for i=1,2,...,n. By considering ordered Banach algebras A and ordered Banach spaces X, we shall establish an order-theoretic version of the Jacobson density theorem.

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