In this lecture we will study the first chapter in the theory of dilations of contractions. To proceed in our study of operator spaces and operator algebras, the material we will cover is not strictly needed. However, this is where I want to begin, for several reasons:
- The objects and theorems here motivate (and have motivated historically) the development of the general theory, and help understand it better and appreciate it more.
- We will reach very quickly a nontrivial application of operator theory to function theory, which is quite different from what you all saw in your studies, probably.
- I am stalling, so that the students who need to fill in some prerequisites (like commutative C*-algebras and the spectral theorem, will have time to do so).
- I love this stuff!
Okay, enough explaining, let us begin.