ABSTRACT

In this paper, we systematically study (slice regular) weighted composition operators on quaternionic Fock spaces. More precisely, the following results are obtained:

1. Some relationship for weighted composition operators between the quaternionic and classical settings is explored to give criteria for boundedness and compactness of weighted composition operators, and to estimate the essential norm, Schatten classes and approximation numbers of such operators.

2. We describe the S-spectra of weighted composition operators, in contrast to the classical case, which reveals some new phenomenons. Concretely, we mainly characterize the S-spectra, essential S-spectra of composition operators; the S-spectra of normal, $\mathcal{C}$-symmetric and compact weighted composition operators.

3. We completely characterize the boundedness, compactness and essential norm of the difference of two weighted composition operators. Moreover, path connected components of the space of nonzero weighted composition operators are characterized too.

摘要

在本文中，我们系统地研究了四元数 Fock 空间上的（切片规则）加权组合算子。更准确地说，得到以下结果：

1. 探索了四元数和经典设置之间的加权复合算子的一些关系，以给出加权复合算子的有界性和紧致性标准，并估计这些算子的基本范数、Schatten 类和近似数。

2. 我们描述了加权合成算子的S谱，与经典情况相反，它揭示了一些新现象。具体来说，我们主要刻画合成算子的S-谱、本质S-谱；正常的S谱，$\mathcal{C}$-对称和紧凑的加权组合算子。

3. 我们完整地刻画了两个加权复合算子之差的有界性、紧致性和本质范数。此外，还表征了非零加权复合算子空间的路径连通分量。