2025/07/26 by Du, Jiaoye, Tong, Cezhong, Yang, Zicong
#30H20 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2507.19735
We first obtain a simpler proof of the main results in [IEOT, \bf 93(2021), 17], which characterized the bounded and compact differences Cu,φ-Cv,ψ of two weighted composition operators acting from Aαp(\mathbbD) to Aαq(\mathbbD). Then we get some characterizations for the difference of weighted composition operator belonging to Schatten class. Moreover, compact difference of a weighted composition operator and a unweighted composition operator on Hardy space is also studied. It shows a rigidity, i.e. Cu,φ-Cψ is compact on H2(\mathbbD) if and only if both Cu',φ:H2(\mathbbD)→ A12(\mathbbD) and Cuφ',φ-Cψ',ψ:A12(\mathbbD)→ A12(\mathbbD) are compact, which generalize a result in [JFA, \bf 278(2020), 108401].