# Functional Version for Furuta Parametric Relative Operator Entropy

## TL;DR

This paper introduces a functional approach to Furuta's parametric relative operator entropy, simplifying the derivation of related inequalities and providing a new perspective on operator entropy analysis.

## Contribution

It presents a novel functional framework for Furuta's operator entropy, enabling straightforward derivation of inequalities and advancing theoretical understanding.

## Key findings

- Functional approach simplifies derivation of operator inequalities
- Theoretical results directly imply operator version inequalities
- Provides new insights into relative operator entropy properties

## Abstract

Functional version for the so-called Furuta parametric relative operator entropy is here investigated. Some related functional inequalities are also discussed. The theoretical results obtained by our functional approach immediately imply those of operator versions in a simple, fast and nice way.