The Jacobson Density Theorem for Non-Commutative Ordered Banach
The Jacobson Density Theorem for Non-Commutative Ordered Banach Algebras
University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
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,...,xn are linearly independent in X and if y1,y2,...,yn are in X, then there exists an a∈ A such that π(a)xi=yi 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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