Essential Normality of automorphic composition operators

2014/08/19 by Liangying Jiang, Jiang, Liangying, Caiheng Ouyang +3
Mathematics · #32A36 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary 47B33 #Secondary 32A35

paper · pdf · doi:10.48550/arxiv.1408.4381

openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first characterize those composition operators that are essentially normal on the weighted Bergman space A²_s(D) for any real s>-1, where induced symbols are automorphisms of the unit disk D. Using the same technique, we investigate the automorphic composition operators on the Hardy space H²(B_N) and the weighted Bergman spaces A²_s(B_N) (s>-1). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball B_N that are not essentially normal.

Related

• Essentially Normal Composition Operators on H²
• Normal, cohyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces
• Commutators of automorphic composition operators with adjoints
• Spectra of weighted composition operators induced by automorphisms
• Isometries of the product of composition operators on weighted Bergman space