2: Paper Source
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Paper's Title:

**
The Jacobson Density Theorem for Non-Commutative Ordered Banach
Algebras**

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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 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
order-theoretic version of the Jacobson density theorem.

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