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<p>Recently, Choe-Koo-Wang (J Funct Anal, 2020, 278) demonstrated the rigid phenomenon: The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC), implies that each difference is compact on the weighted Bergman space in the unit disk. Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces, Korenblum spaces and bounded holomorphic function spaces, we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball. Furthermore, we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition (CNC) on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.</p>

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Compact linear combinations of composition operators on the unit ball

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • Chunyu Dong,
  • Xin Guo,
  • Qijian Kang

摘要

Recently, Choe-Koo-Wang (J Funct Anal, 2020, 278) demonstrated the rigid phenomenon: The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC), implies that each difference is compact on the weighted Bergman space in the unit disk. Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces, Korenblum spaces and bounded holomorphic function spaces, we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball. Furthermore, we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition (CNC) on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.