An Introduction to the Shift Operator
Abstract: The aim of this project is to serve as an introduction to the theory of the shift operatorSdefined onthe sequence space l^2 by shifting the sequence 1 step to the right i.e. S{x0,x1,...}={0,x0,x1,...}. The main focus of the project is to familiarize the reader with the theory necessary to understand and prove a specific theorem of the shift operator called Beurling’s theorem, an important result that characterizes all closed shift invariant subspaces of l^2. A subspace A of l^2 is said to be shift invariant if for all x∈A Sx∈A
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