Abstract
For ϕ \phi in H ∞ {H^\infty } , let T ϕ {T_\phi } be the analytic Toeplitz operator with symbol ϕ \phi and let { T ϕ } ′ \{ {T_\phi }\} ’ be the commutant of T ϕ {T_\phi } . Two infinite Blaschke products ϕ \phi and ψ \psi , are exhibited such that { T ϕ } ′ ∩ { T ψ } ′ \{ {T_\phi }\} ’ \cap \{ {T_\psi }\} ’ is not equal to { T θ } ′ \{ {T_\theta }\} ’ for any inner function θ \theta . Also, two questions on reducing subspaces of analytic Toeplitz operators are answered.
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