Decomposition of Positive Projections on C*-Algebras.
Let be a prime ring with its Utumi ring of quotients and extended centroid . Suppose that is a generalized derivation of and is a noncentral Lie ideal of such that for all , where is a fixed integer. Then one of the following holds:
Let be a Jordan-Banach algebra with identity 1, whose norm satisfies:(i) , (ii) (iii) . is called a JB algebra (E.M. Alfsen, F.W. Shultz and E. Stormer, Oslo preprint (1976)). The set of squares in is a closed convex cone. is a complete ordered vector space with as a order unit. In addition, we assume to be monotone complete (i.e. coincides with the bidual ), and that there exists a finite normal faithful trace on .Then the completion of with respect to the Hilbert structure...
We study discontinuous invertibility preserving linear mappings from a Banach algebra into the algebra of n × n matrices and give an explicit representation of such a mapping when n = 2.