A non-selfadjoint Russo-Dye Theorem.
Continuous measures on compact Lie groups
We study continuous measures on a compact semisimple Lie group using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if is a compact set of continuous measures on there exists a singular measure such that is absolutely continuous with respect to the Haar measure on...
Shift Оperators
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...
Preface
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