In this article we introduce the generalized DIFFERENCE paranormed SEQUENCE SPACES Co (Dn, L, P), C (Dn, L, P) and L¥ (Dn, L, P) associated with the multiplier SEQUENCE L=(lk) of nonzero complex numbers. We study their different properties and prove some inclusion relations.

In this paper, we determine the upper and lower bounds for the norm of lower triangular matrix operators on Cesà, ro weighted (p, v)−, fractional DIFFERENCE SEQUENCE SPACES of modulus functions. We consider the matrix operators acting between ℓ, p(w) and Cp(v, ω, , Δ, (η, , ℓ, ), F) and identify their bounds and vice-versa. We also investigate the same characteristics for Nö, rlund and weighted mean matrix operators.

In this paper we first introduce $\bar{N}_{\Delta^{-}}^{q}$ summable DIFFERENCE SEQUENCE SPACES and prove some properties of these SPACES. We then obtain the necessary and sufficient conditions for infinite matrices $A$ to map these SEQUENCE SPACES on the SPACES $c_0, c$ and $\ell_\infty$, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these SPACES.

In this paper we investigate the cyclicity of the multiplication operator Mz acting on the weighted Hardy SPACES of formal Laurent series.

Let {b (n)}¥n = -¥ be a SEQUENCE of positive numbers such that b(0) =1 and let 1<p<¥. We consider the space of all formal Laurent series f (z) = S¥n=-¥ f^ (n) zn such thatS¥n=-¥|f^ (n) |p b (n)p<¥.We investigate the supercyclicity with respect to a SEQUENCE on the Banach SPACES of formal Laurent series.