Abstract. We introduce the concept of non-positive operators with respect to a fixed operator defined between two real normed linear spaces. Significantly, we observe that, in certain cases, it is possible to study such type of operators from a geometric point of view. As an immediate application of our study, we explicitly characterize certain classes of non-positive operators between particular pairs of real normed linear spaces. Furthermore, we present a complete characterization of smooth and strictly convex Radon planes in connection with non-positive operators.

DOI: 10.14232/actasm-019-554-z

AMS Subject Classification (1991): 47L05, 46B20

Keyword(s): Birkhoff--James orthogonality, semi-inner-product, non-positive operator, polyhedral Banach spaces

received 23.10.2019, revised 5.8.2020, accepted 11.8.2020. (Registered under 54/2019.)