instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Compact Composition Operators and Deddens Algebras
We consider the Deddens algebras associated to compact composition operators on the Hardy space H2 on the unit disk. When the compact composition operator corresponds to a function ϕ that satisfies ϕ(0) = 0 and ϕ 0 (0) 6= 0, we show that the lattice of invariant subspaces of this algebra is {0} ∪ {z n : n ∈ N0}. As a consequence, for this class of operators the associated Deddens algebra is weakly dense in the algebra of lower triangular matrices.