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Journal of Operator Theory

Volume 67, Issue 2, Spring 2012  pp. 581-604.

A semigroup composition C-algebra

Authors Katie S. Quertermous
Author institution: Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, U.S.A.

Summary:  For 0<s<1, let φs(z)=sz+(1s). We investigate the unital C-algebra generated by the semigroup {Cφs:0<s<1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point spectrum of a related collection of operators and show that the quotient of the C-algebra by its commutator ideal is isomorphic to the direct sum of \IC and the algebra of almost periodic functions on the real line. In addition, we show that the C-algebra is irreducible.


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