Abstract
In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces
c
e
s
φ
, where
φ
is an Orlicz function such that the class
S
c
e
s
φ
of all bounded linear operators between arbitrary Banach spaces with its sequence of
s
-
numbers which belong to
c
e
s
φ
forms an operator ideal. The completeness and denseness of its ideal components are specified and
S
c
e
s
φ
constructs a pre-quasi Banach operator ideal. Some inclusion relations between the pre-quasi operator ideals and the inclusion relations for their duals are explained. Moreover, we have presented the sufficient conditions on
c
e
s
φ
such that the pre-quasi Banach operator ideal generated by approximation number is small. The above results coincide with that known for
c
e
s
p
(
1
<
p
<
∞
)
.