In this paper, we study composition operators on generalized Fock spaces of slice hyperholomorphic functions. More precisely, some relationship for composition operators between the slice hyperholomorphic setting and the classical setting is explored to characterize the boundedness and compactness of composition operators. Motivated by a question in Kumar (Adv Appl Clifford Algebras 27:1459–1477, 2017), we characterize S-spectra of composition operators. Finally, we characterize connected components of the space of bounded composition operators.

中文翻译：

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切片超亚纯函数的广义Fock空间上的复合算子

在本文中，我们研究了切片超亚纯函数的广义Fock空间上的合成算子。更精确地，探索了切片超全同性设置和经典设置之间的一些合成算子关系，以表征合成算子的有界性和紧致性。受Kumar（Adv Appl Clifford Algebras 27：1459-1477，2017）中一个问题的激励，我们对合成算子的S谱进行了刻画。最后，我们刻画了有界合成算子空间的连通分量。