An order-preserving linear map from matrices to banach ∗-algebras and applications

Chansangiam, Pattrawut

doi:10.1155/2013/328510

An order-preserving linear map from matrices to banach ∗-algebras and applications

Author(s)

Chansangiam, Pattrawut

Date Issued

January 1, 2013

Type

Article

DOI

10.1155/2013/328510

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.

Citation

Journal of Mathematics, 2013, 2013