Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 41, No 1, (2015), 35p-48p
Shift operators play an important role in different areas of Mathematics such as Operator Theory, Dynamical Systems and Complex Analysis. In these lectures we discuss basic properties of these operators. We present Beurling’s Theorem which describes the invariant subspaces of the shift. The structure of the C *-algebra generated by the shift is described. We also indicate how the shift operators appear in the analysis of isometries on a Hilbert space: Wold decomposition and Coburn’s theorem. 2010 Mathematics Subject Classification: Primary 46L05; Secondary 47A15, 47B35.