Compact Differences of Composition Operators in Several Variables

By Katherine C. Heller, Barbara D. Maccluer, Rachel J. Weir. 2010

72 citations recorded by the source corpus.

When φ and ψ are linear–fractional self-maps of the unit ball BN in $${{\mathbb C}^N,N\geq 1}$$, we show that the difference $${C_{\varphi}-C_{\psi}}$$ cannot be non-trivially compact on either the Hardy space H2(BN) or any weighted Bergman space $${A^2_{\alpha}(B_N)}$$. Our arguments emphasize geometrical properties of the inducing maps φ and ψ.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3307af72637386c8a49c69dd996f09781282d572

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In Applied Mathematics

1. B. Choe
2. Inyoung Park
3. H. Koo

Citations in the corpus

• Compact Differences of Composition Operators on the Bergman Spaces Over the Ball (2013, background): “In case p = 2, the following characterization is independently proved by Heller, MacCluer and Weir [6] and Jiang and Ouyang [7].”