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.
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Communicated by L. Molnár
Acknowledgment.
The authors convey their sincere thanks to the referees for their valuable comments and suggestions. The research of the first named author is supported by the Mathematical Research Impact Centric Support (MATRICS) grant, File No :MTR/2019/000640, by the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India. The research of Dr. Sain is sponsored by Dr. D. S. Kothari Postdoctoral Fellowship. Dr. Sain feels elated to acknowledge the loving presence of his childhood friend and brother-in-arms Mr. Arijeet Mukherjee, an accomplished traveler, in every sphere of his life. The third named author acknowledges with thanks for financial support under Institute Post Doctoral Fellowship (IITG/R &D/IPDF/2017-2018/MA01) of Indian Institute of Technology Guwahati.
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Chattopadhyay, A., Sain, D. & Senapati, T. A study of non-positive operators between real normed linear spaces. ActaSci.Math. 86, 449–466 (2020). https://doi.org/10.14232/actasm-019-554-z
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DOI: https://doi.org/10.14232/actasm-019-554-z