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- W2037648328 abstract "A bounded operator T on a separable Hilbert space H is said to be complex symmetric if there exists an orthonormal basis for H with respect to which T has a self-transpose matrix representation. In this paper, we study the complex symmetry of composition operators C ϕ f = f ∘ ϕ induced on the Hardy space H 2 by holomorphic self-maps ϕ of the open unit disk D . For any holomorphic self-map ϕ of D , we establish that if C ϕ is complex symmetric, then ϕ must fix a point in D . Thus among the automorphisms of D , only the elliptic ones may induce complex symmetric composition operators. For an elliptic automorphism ϕ , we prove that if ϕ is not a rotation or of order 3, then C ϕ is complex symmetric if and only if ϕ ( z ) = α − z 1 − α ¯ z for some α ∈ D ∖ { 0 } ." @default.
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- W2037648328 date "2015-09-01" @default.
- W2037648328 modified "2023-09-24" @default.
- W2037648328 title "Complex symmetry of invertible composition operators" @default.
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- W2037648328 doi "https://doi.org/10.1016/j.jmaa.2015.04.008" @default.
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