Abstract
We suggest a sufficient setting on any linear space of sequences
V
such that the class
B
V
s
of all bounded linear mappings between two arbitrary Banach spaces with the sequence of
s
-numbers in
V
constructs a map ideal. We define a new sequence space
(
ces
r
1
,
r
2
t
)
υ
for definite functional
υ
by the domain of
(
r
1
,
r
2
)
-Cesàro matrix in
ℓ
t
, where
r
1
,
r
2
∈
(
0
,
∞
)
and
1
≤
t
<
∞
. We examine some geometric and topological properties of the multiplication mappings on
(
ces
r
1
,
r
2
t
)
υ
and the pre-quasi ideal
B
(
ces
r
1
,
r
2
t
)
υ
s
.