Slice regular weighted composition operators

Abstract

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