p-adic Magic Contractions, p-adic von Neumann Inequality and p-adic Sz.-Nagy Dilation

TL;DR

This paper introduces the concept of p-adic magic contractions on p-adic Hilbert spaces and establishes key dilation and inequality results analogous to classical operator theory.

Contribution

It develops the theory of p-adic magic contractions and proves p-adic versions of fundamental dilation and inequality theorems.

Findings

Introduction of p-adic magic contraction concept

Derivation of p-adic Halmos dilation and Sz.-Nagy dilation

Establishment of p-adic von Neumann inequality

Abstract

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.