Regularly limited, Grothendieck, and Dunford--Pettis operators

Abstract

Various types of compactness in Banach spaces were in streamline of functional analysis in the second half of the 20th century. At some point, in order to diversify the classes of compact operators, the Banach lattice structure had come in play by Meyer-Nieberg, Dodds, Fremlin, Aliprantis, Wickstead, and others. In the present paper, we continue this line of study with main emphasis on regularity of operators under the investigation.