# Extreme contractions on finite-dimensional polygonal Banach spaces-II

## TL;DR

This paper introduces the weak L-P property for Banach space pairs, explores its implications for extreme contractions, and computes exact numbers of such contractions in specific polygonal Banach spaces.

## Contribution

It defines the weak L-P property, provides examples, and applies it to determine the exact count of extreme contractions between certain polygonal Banach spaces.

## Key findings

- Examples of pairs satisfying or not satisfying weak L-P property
- Exact number of extreme contractions in specific polygonal Banach spaces
- Analysis of the optimality of the weak L-P property results

## Abstract

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.