This research report serves as an introduction to the concept of Operator
Spaces which has gained considerable momentum in its acknowledgement and
research interest in the last few decades. It will highlight a very important
breakthrough on the characterization of Operator spaces which occurred in
the !ast few years brought about by Z.J. Ruan. It investigates the relationship
of this space in relation to Banach space theory by looking at an extension
theorem for linear functionals,
