Compact differences of composition operators

2010/06/10 by Katherine Heller, Heller, Katherine, Barbara D. MacCluer +3
Mathematics · #47B33 #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:47B33

paper · pdf · doi:10.48550/arxiv.1006.2121

20 pages

arxiv created 2010/06/10 · openalex publication_date 2010/06/10 · arxiv updated 2010/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

When φ and ψ are linear-fractional self-maps of the unit ball B_N in \mathbb C^N, N≥ 1, we show that the difference C_φ-C_ψ cannot be non-trivially compact on either the Hardy space H²(B_N) or any weighted Bergman space A²_α(B_N). Our arguments emphasize geometrical properties of the inducing maps φ and ψ.

Related

• Compact Differences of Composition Operators on Holomorphic Function Spaces in the Unit Ball
• Commutators of automorphic composition operators with adjoints
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• Difference of weighted composition operators between Bergman spaces