# 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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