


Paper Title:
The Jacobson Density Theorem for NonCommutative Ordered Banach Algebras
Author(s):
Kelvin Muzundu
University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
Zambia.
Email: kmzundu@gmail.com
Abstract:
The Jacobson density theorem for general noncommutative Banach algebras states as follows: Let π be a continuous, irreducible representation of a noncommutative Banach algebra A on a Banach space X. If x_{1},x_{2},...,x_{n} are linearly independent in X and if y_{1},y_{2},...,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 ordertheoretic version of the Jacobson density theorem.
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