Aleksandrov Measures used in Essential Norm Inequalities for Composition Operators

By Jonathan E. Shapiro

This paper appears in the Journal of Operator Theory, 40 (1998), 133-146.


Recently, Aleksandrov measures have been used to find new formulas for the essential norms of composition operators. Here it is shown how these measures also provide information about the essential norm of the difference of two composition operators. The utility of the Aleksandrov--measure approach to the study of composition operators is illustrated in the final section of this paper, where these measures are used to supply new proofs of several known results.

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