Some q-Bell sequence spaces associated with c and c₀

In this work, we give some topological properties of the sequence spaces ₚ(Bq) ℓ p ( B ˆ q ) (with $0< p<1$ 0 < p < 1 ), c₀(Bq) c 0 ( B ˆ q ) , c(Bq) c ( B ˆ q ) , and ∞(Bq) ℓ ∞ ( B ˆ q ) defined by the matrix Bq B ˆ q . Furthermore, we construct bases for the space c₀(Bq) c 0 ( B ˆ q ) and c(Bq) c ( B ˆ q ) , determine α -, β -, γ -duals of the above defined spaces, classify some matrix classes and provide several results related to compactness of certain matrix operators on the space c₀(Bq) c 0 ( B ˆ q ) .