A study of 2-Toeplitz operator on Köthe spaces

Abstract This paper presents the concept of the 2-Toeplitz operator on Köthe spaces, which is a subclass of Fréchet spaces that has recently gained significant prominence in the study of functional analysis and operator theory. We establish detailed characterizations of the continuity and compactness of this operator, providing both necessary and sufficient conditions. Additionally, several concrete examples are provided to illustrate the theoretical results.