Variations of completely bounded maps on operator spaces

TL;DR

This paper introduces and studies new classes of maps on operator spaces, including weighted cb maps and $\Lambda_\mu$-cb maps, along with their properties and associated tensor products.

Contribution

It generalizes the concept of completely bounded maps and bilinear maps on operator spaces, providing a broader framework and new tensor product constructions.

Findings

Defined weighted cb maps and $\Lambda_\mu$-cb maps.

Analyzed properties of these maps.

Developed an associated operator space tensor product.

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.