In the present paper we essentially deal with to determine the neccessary and sufficient conditions in order for a matrix
A=(
ank) to belong to the classes (
Xp:
bs), (
Xp:
fs), (
X1:
lp), (
Xp:
X1) and (
lp:
X1), respectively. Furthermore, we give the sufficient conditions on a matrix
A=(
ank) in the class (
Xp:
lp) for 1<p<∞ and prove a Steinhaus type theorem concerning the disjointness of the classes (
Xp:
fs)
r and (
bs:
fs). Those sequence spaces are described, below.
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