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2009•Abstract and Applied AnalysisOpen access

On the Norm of Certain Weighted Composition Operators on the Hardy Space

Mahmood Haji Shaabani, B. Khani Robati

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Abstract

We obtain a representation for the norm of certain compact weighted composition operator Cψ,φ on the Hardy space H2, whenever φ(z) = az + b and ψ(z) = az − b. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on φ and ψ. Moreover, we characterize the norm and essential norm of such operators in a special case.

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We obtain a representation for the norm of certain compact weighted composition operator Cψ,φ on the Hardy space H2, whenever φ(z) = az + b and ψ(z) = az − b. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on φ and ψ. Moreover, we characterize the norm and essential norm of such operators in a special case.

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Available abstract

We obtain a representation for the norm of certain compact weighted composition operator Cψ,φ on the Hardy space H2, whenever φ(z) = az + b and ψ(z) = az − b. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on φ and ψ. Moreover, we characterize the norm and essential norm of such operators in a special case.

Key concepts: Mathematics, Norm (philosophy), Operator norm, Dual norm, Hardy space, Pure mathematics, Algebra over a field, Operator theory

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