WEIGHTED COMPOSITION OPERATORS ON L('2)
Abstract
An operator T on L('2) is a weighted composition operator if there are functions g from the integers into the integers and u from the integers into the complex numbers such that Tf(n) = u(n) (f(CCIRC)g(n)) for all f in L('2) and all n in the integers. In this work the properties of weighted composition operators on L('2) have been studied. In addition to several elementary results, such as the norm of T, when T is normal, and so forth, the three major results obtained are: determining the spectrum of T, determining the reducing subspaces of T, and classifying weighted composition operators up to unitary equivalence. To obtain complete results it was necessary to assume the composition function g had finitely many branches.
Degree
Ph.D.
Subject Area
Mathematics
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