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2006•Houston journal of mathematicsRequires access

Automorphic Composition Operators on Hardy and Bergman Spaces in the Ball

Barbara D. McCluer, Matthew A. Pons

Open publisher page 8 citations

Abstract

We determine which composition operators with automorphism symbol are essentially normal on the Hardy and Bergman space of the ball. To do this, we first show that modulo the compact operators, the product of an automorphic composition operator followed by its adjoint is a Toeplitz operator with positive symbol.

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What this paper is about

We determine which composition operators with automorphism symbol are essentially normal on the Hardy and Bergman space of the ball. To do this, we first show that modulo the compact operators, the product of an automorphic composition operator followed by its adjoint is a Toeplitz operator with positive symbol.

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Available abstract

We determine which composition operators with automorphism symbol are essentially normal on the Hardy and Bergman space of the ball. To do this, we first show that modulo the compact operators, the product of an automorphic composition operator followed by its adjoint is a Toeplitz operator with positive symbol.

Key concepts: Mathematics, Composition operator, Modulo, Bergman space, Bergman kernel, Hardy space, Toeplitz matrix, Automorphism

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