Every z-linear maps is a functional p-convex

TL;DR

This paper proves that every z-linear map is a functional p-convex, utilizing established lemmas and theorems to demonstrate the relationship between these mathematical concepts.

Contribution

It establishes a new equivalence between z-linear maps and functional p-convexity, expanding understanding in functional analysis.

Findings

Every z-linear map is a functional p-convex.

Uses lemmas by Kalton and Peck, and theorems by Aoki and Rolewicz.

Provides a proof based on the triangle inequality.

Abstract

The main result of the paper is the following: Every $z$-linear maps is a functional p-convex. We will prove this statement using lemma developed by Kalton and Peck [6] and theorem developed by Aoki and Rolewicz.Based on the definition of functional and using the tool of the triangle inequality prove the following theorem.