Journal of Operator Theory

Volume 84, Issue 1, Summer 2020 pp. 127-137.

Extreme contractions on finite-dimensional polygonal Banach spaces. II

Authors: Anubhab Ray

$1$ , Saikat Roy

$2$ , Satya Bagchi

$3$ , Debmalya Sain

$4$
Author institution:

$1$ Department of Mathematics, Jadavpur University, Kol-kata, 700032, India

$2$ Department of Mathematics, National Institute of Technology Durgapur, Durgapur, 713209, India

$3$ Department of Mathematics, National Institute of\break Technology Durgapur, Durgapur, 713209, India

$4$ Department of Mathematics, Indian Institute of Science, Bengaluru, 560012, India

Summary: We introduce the concept of weak L-P property for a pair of Banach spaces, in the study of extreme contractions. We give examples of pairs of Banach spaces

$not$ satisfying weak L-P property and apply the concept to compute the exact number of extreme contractions between a particular pair of polygonal Banach spaces. We also study the optimality of our results on the newly introduced weak L-P property for a pair of Banach spaces, by considering appropriate examples.

DOI: http://dx.doi.org/10.7900/jot.2019jan23.2253
Keywords: extreme contractions, polygonal Banach spaces, L-P property

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