Journal of Operator Theory
Volume 67, Issue 2, Spring 2012 pp. 581-604.
A semigroup composition C∗-algebraAuthors: 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+(1−s). 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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