Kalaichelvan, Rajendra2018-10-292018-10-291993https://hdl.handle.net/10539/25912A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science.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,enLinear topological spaces.Operator theory.Matrices.Thesis