A Semigroup Composition C*-algebra

Details A Semigroup Composition C*-algebra A Semigroup Composition C*-algebra

2009-09-04

arxiv.org/abs/0909.0956v1

Mathematics

Functional Analysis

21 pages

Scientific paper

For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 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 the complex numbers 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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