# Simultaneous universality

## TL;DR

This paper introduces the concept of simultaneous universality for operators, providing criteria and applications mainly in sequence spaces and spaces of holomorphic functions.

## Contribution

It defines simultaneous universality, relates it to existing concepts, and offers new criteria and applications in functional analysis.

## Key findings

- Criteria for simultaneous universality established
- Applications to operators in sequence spaces
- Connections to classical universality concepts

## Abstract

In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint universality. Several criteria are provided, and several applications to specific operators or sequences of operators are performed, mainly in the setting of sequence spaces or spaces of holomorphic functions.