Statistical extension of bounded sequence space

Authors : Maya ALTINOK, Mehmet KÜÇÜKASLAN, Umutcan KAYA

Pages : 82-99

Doi:10.31801/cfsuasmas.736132

View : 16 | Download : 21

Publication Date : 2021-06-30

Article Type : Research Paper

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 shown that 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 $l_{\infty}^{st}$.
Keywords : Natural density, statistical convergence, statistical sup norm