The essential norms of composition operators
نویسندگان
چکیده
منابع مشابه
The Essential Norms of Composition Operators between Generalized Bloch Spaces in the Polydisc and Their Applications
Let Un be the unit polydisc of Cn and φ = (φ1, . . . ,φn) a holomorphic self-map of Un. p(Un), p 0 (U n), and p 0∗(U n) denote the p-Bloch space, little p-Bloch space, and little star p-Bloch space in the unit polydisc Un, respectively, where p,q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between p(Un) ( p 0 (U n) or p 0∗(U n)) an...
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We obtain a representation for the norm of the composition operator Cφ on the Hardy space H 2 whenever φ is a linear-fractional mapping of the form φ(z) = b/(cz + d). The representation shows that, for such mappings φ, the norm of Cφ always exceeds the essential norm of Cφ. Moreover, it shows that a formula obtained by Cowen for the norms of composition operators induced by mappings of the form...
متن کاملEssential norms of weighted composition operators on the space H∞ of Dirichlet series
We estimate the essential norm of a weighted composition operator relatively to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space H∞ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.
متن کاملEssential Norms of Weighted Composition Operators between Hardy Spaces in the Unit Ball
Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic self-map of Bn and ψ(z) a holomorphic function on Bn, and H(Bn) the class of all holomorphic functions on Bn, where Bn is the unit ball of C , the weight composition operator Wψ,φ is defined by Wψ,φ = ψf(φ) for f ∈ H(Bn). In this paper we estimate the essential norm for the weighted composition operator Wψ,φ acting from the Hardy space H to H (...
متن کاملNorms of Composition Operators on the Hardy Space
Research supported in part by National Science Foundation grant DMS-9401206. Appel and Thrall were supported by the Foundation's REU program for work they performed as undergraduate assistants to Bourdon. We show that the norm of a composition operator on the classical Hardy space H2 cannot be computed using only the set of H2 reproducing kernels, answering a question raised by Cowen and MacCluer.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1992
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500008661