# An indefinite range inclusion theorem for triplets of bounded linear operators on a Hilbert space

## TL;DR

This paper investigates triplets of bounded linear operators on a Hilbert space, establishing a range inclusion theorem with norm estimates using Kren space geometry and de Branges-Rovnyak space theory.

## Contribution

It introduces a new range inclusion theorem for operator triplets, combining Kren space geometry and de Branges-Rovnyak space theory to derive norm estimates.

## Key findings

- Established a range inclusion theorem with norm bounds
- Applied Kren space geometry in operator analysis
- Utilized de Branges-Rovnyak space theory for operator inequalities

## Abstract

We study triplets of Hilbert space operators satisfying a certain inequality. A range inclusion theorem with norm estimate for those triplets is given with the language of Kre\u{\i}n space geometry and de Branges-Rovnyak space theory.