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arXiv · 1305.1610

Positive linear functionals on BP*-algebras

M. El Azhari
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Abstract

Let A be a BP*-algebra with identity e, P_{1}(A) be the set of all positive linear functionals f on A such that f(e) = 1, and let M_{s}(A) be the set of all nonzero hermitian multiplicative linear functionals on A. We prove that M_{s}(A) is the set of extreme points of P_{1}(A). We also prove that, if M_{s}(A) is equicontinuous, then every positive linear functional on A is continuous. Finally, we give an example of a BP*-algebra whose topological dual is not included in the vector space generated by P_{1}(A), which gives a negative answer to a question posed by M. A. Hennings.

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M. El Azhari. 2013-05-07. Positive linear functionals on BP*-algebras. https://arxiv.org/abs/1305.1610

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