Composition operators on a functional Hilbert space
Copyright policy )Composition operators on a functional Hilbert space
Let T be a mapping from a set X into itself and let H(X) be a functional Hilbert space on the set X. Then the composition operator CT on H(X) induced by T is a bounded linear transformation from H(X) into itself defined by CTf = f ∘ T. In this paper composition operators are characterized in the case when H(X) = H2(π+) in terms of the behaviour of the inducing functions in the vicinity of the point at infinity. An estimate for the lower bound of ∥CT∥ is given. Also the invertibility of CT is characterized in terms of the invertibility of T.
- University of Jammu India
Linear operators on function spaces (general), composition operators in Hardy spaces, invertibility, boundedness, \(H^p\)-classes, \(H^p\)-spaces
Linear operators on function spaces (general), composition operators in Hardy spaces, invertibility, boundedness, \(H^p\)-classes, \(H^p\)-spaces
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