C*-modules and operator spaces
This chapter has three main goals. First, to examine Hilbert C*-modules (and their W*-algebra variant, W *-modules) as operator modules. It aims to show that the theory of C *-modules fits comfortably into the operator module framework. Second, to consider space X. In particular, it will discuss the noncommutative Shilov boundary ☐(X) of X. TRO methods and this Shilov boundary provide important insights into the structure of X. Third, to illustrate how C*-module and TRO methods can lead to interesting results about operator spaces. Notes and historical remarks are presented at the end of the chapter.
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