# On Orbit Reflexive Tuple of Operators And Weak Orbit Reflexivity

## TL;DR

This paper investigates conditions for orbit reflexivity of tuples of commuting bounded linear operators on Banach spaces and introduces the concept of weak orbit reflexivity, expanding the understanding of operator behavior.

## Contribution

It provides new conditions for orbit reflexivity of operator tuples and introduces the notion of weak orbit reflexivity in Banach spaces.

## Key findings

- Established various conditions for orbit reflexivity.
- Introduced the concept of weak orbit reflexivity.
- Presented results connecting weak orbit reflexivity with existing theory.

## Abstract

In this paper we give a various conditions for which the tuple $\mathcal{T} = (T_{1} , T_{2} , ... , T_{n})$ of commutative bounded linear operators on an infinite dimensional ( real , complex ) Banach space X is orbit reflexive. After we introduce the notion of weak orbit reflexive operator and we show some results.