Composition operators and Aleksandrov-Clark measures

Sam Elliott (Leeds)

Tuesday 28th April, 2009 16:00-17:00 214


On a number of Banach spaces of functions, it is useful to define an operator derived from pre-composition with some self-map of the domain. Such an operator is naturally called a composition operator, and the map from which it is derived is called its symbol. The first section of this talk will be an introduction to these operators, and to some of the spaces in which they are most relevant. The second section of the talk will deal with the increasingly studied question of finding adjoint formulae for such operators, and will introduce the concept of Aleksandrov-Clark measures as a useful tool for this procedure. If time permits, a third section will include more recent results which give a meaningful definition of the measures for a different class of spaces, and may touch on a more explicit formula, derived using integral methods, for adjoints of composition operators with certain special symbols.

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