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An Order-Preserving Linear Map from Matrices to Banach * -Algebras and Applications

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  • Pattrawut Chansangiam

Abstract

We establish a theorem for which a number of absolute-value identities and inequalities in the framework of Banach -algebras can be generated. To do this job, we construct an order-preserving linear map from the vector space of 2-by-2 hermitian matrices to a hermitian Banach -algebras. This map can convert any suitable matrix ordering to a number of identities and inequalities in Banach -algebras. Hence, we obtain a number of analogues of the well-known results in a framework of hermitian Banach -algebras.

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  • Pattrawut Chansangiam, 2013. "An Order-Preserving Linear Map from Matrices to Banach * -Algebras and Applications," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, January.
    • Handle: RePEc:hin:jjmath:328510
    DOI: 10.1155/2013/328510
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