Some topological properties of nonlinear positive mappingsbetween C -algebras

It is known that every positive linear map between unital C -algebras is norm-normcontinuous. However, this is not necessarily true in the setting of nonlinear positive mapsbetween C -algebras, in general. In this talk, we present some conditions to provide thecontinuity of nonlinear positive maps between C -algebras with respect to the strong andnorm operator topologies. These results imply the automatic continuity of a large familyof nonlinear positive maps between C -algebras. Moreover, we show that in some classes ofnonlinear positive maps the continuity property implies the operator monotonicity.

کلیدواژه ها:

nonlinear positive map ، n-monotone map ، continuity ، strong operator topology.