Statistical extension of bounded sequence space

Abstract

In this paper by using natural density real valued bounded sequence space $l_{infty}$ is extented and statistical bounded sequence space $l_{infty}^{st}$ is obtained. Besides the main properties of the space $l_{infty}^{st}$, it is shown that $l_{infty}^{st}$ is a Banach space with a norm produced with the help of density. Also, it is shownthat there is no matrix extension of the space $l_{infty}$ that its bounded sequences space covers $l_{infty}^{st}$. Finally, it is shown that the space $l_{infty}$ is a non-porous subset of $l_{infty}^{st}$.