2009/09/04 by Katie S. Quertermous, Quertermous, Katie S.
Mathematics · #47B33 (Primary) 47B20 #47B35 #47L80 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47B20 #msc:47B33 #msc:47B35 #msc:47L80
paper · pdf · doi:10.48550/arxiv.0909.0956
21 pages
arxiv created 2009/09/04 · arxiv updated 2009/12/01
For 0 < s < 1, let phis(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup Cphis : 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.