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Published online by Cambridge University Press: 10 February 2020
This chapter is an excursion into what could be called the local theoryof operator spaces. Here the main interest is on finite dimensional operator spaces and the degree of isomorphism of the various spaces is estimated using the c.b. analogue of the Banach-Mazur distance from Banach space theory. The main result is that the metric space formed of all the n-dimensional operator spaces equipped with the latter cb-distance is non separable for any n>2. This is in sharp contrast with the Banach space analogue which is a compact metric space.
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