Statistical extension of bounded sequence space
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Date
2021-06-30
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi Fen Fakültesi
Abstract
In this paper by using natural density real valued bounded sequence space
l
∞
is extented and statistical bounded sequence space
l
s
t
∞
is obtained. Besides the main properties of the space
l
s
t
∞
, it is shown that
l
s
t
∞
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
∞
that its bounded sequences space covers
l
s
t
∞
. Finally, it is shown that the space
l
∞
is a non-porous subset of
l
s
t
∞
.
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Keywords
Natural density, Statistical convergence, Statistical sup norm