Variations of completely bounded maps on operator spaces

Abstract

We introduce weighted cb maps and $\Lambda_\mu$-cb maps on operator spaces which are generalizations of completely bounded maps and a certain class of bilinear maps on operator spaces which we call $\lambda_\mu$-cb bilinear maps. Some basic properties of these maps and an operator space tensor product associated to $\lambda_\mu$-cb bilinear maps have been studied.