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

Abstract EN

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.