On matrix mappings into some strong Cesàro sequence spaces

We determine the classes (X, Y_T) of matrix transformations from X into Y_T where X is one of the classical sequence spaces c₀, c, ?_∞ and ?₁ of all null, convergent and bounded complex sequences and all absolutely convergent complex series, T is a triangle, Y_T is the matrix domain of T in Y and Y is any of the sets of all sequences that are summable, summable to zero or bounded by the strong Cesàro method of order 1, with index 1 ? p < ∞. Furthermore, we determine the representations of the general bounded linear operators from c into Y. We also establish estimates for the norms of the operators in each case.     

Another look at Cesàro sequence spaces

We consider the Cesàro sequence space cesp as a closed subspace of the infinite ?p-sum of finite dimensional spaces. We easily obtain many known results, for example, cesp has property (β) of Rolewicz, uniform Opial property, and weak uniform normal structure. We also consider some generalized Cesàro sequence spaces. Finally, we compute the von Neumann-Jordan and James constants of the two-dimensional Cesàro sequence space when 1<p?2.     

On the James constant and B-convexity of Cesàro and Cesàro-Orlicz sequence spaces

The classical James constant and the nth James constants, which are measure of B-convexity for the Cesàro sequence spaces cesp and the Cesàro-Orlicz sequence spaces cesM, are calculated. These investigations show that cesp,cesM are not uniformly non-square and even they are not B-convex. Therefore the classical Cesàro sequence spaces cesp are natural examples of reflexive spaces which are not B-convex. Moreover, the James constant for the two-dimensional Cesàro space is calculated.     

A note on Cesàro-Orlicz sequence spaces

The condition δ₂ in Cesàro-Orlicz sequence spaces equipped with the Luxemburg norm is discussed. The comparison theorem for these spaces is presented. Some counterexamples are provided.     

A short proof of some recent results related to Cesàro function spaces

We give a short proof of the recent results that, for every 1≤p<∞$1\le p<\infty$, the Cesàro function space Ce_sp(I)$Ce{s}_p\left(I\right)$ is not a dual space, has the weak Banach–Saks property and does not have the Radon–Nikodym property.     

On some new paranormed euler sequence spaces and Euler Core

In this paper, the sequence spaces e0^τ（u, p） and ec^τ（u, p） of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e0^τ（u,p） and ec^τ（u,p） are linearly isomorphic to spaces co（p） and c（p）, respectively. Furthermore, the α-, β- and γ-duals of the spaces 0^τ（u,p） and ec^τ（u,p） have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices （e0^τ）（u, p） ： μ） has been characterized, where μ is one of the sequence spaces l∞, c and co and derives the other characterizations for the special cases of μ. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.     

On some new generalized sequence spaces

In this paper we define the sequence sets ?_∞(u,Δ²,p), c(u,Δ²,p) and c₀(u,Δ²,p), and give α- and β-duals of these sets. Further we investigate matrix transformations in the spaces and give a characterization of the class (?_∞(u,Δ²,p),?_∞).     

Generalized difference sequence spaces and their dual spaces

The definition of the pα-, pβ- and pγ-duals of a sequence space was defined by Et [Internat. J. Math. Math. Sci. 24 (2000) 785-791]. In this paper we compute pα- and N-duals of the sequence spaces Δ^m_v(X) for X=?_∞, c and c₀, and compute β- and γ-duals of the sequence spaces Δ^m_v(X) for X=?_∞, c and c₀.     

Some new spaces of double sequences

In this study, we define the double sequence spaces BS, BS(t), CSp, CSbp, CSr and BV, and also examine some properties of those sequence spaces. Furthermore, we show that these sequence spaces are complete paranormed or normed spaces under some certain conditions. We determine the α-duals of the spaces BS, BV, CSbp and the β(?)-duals of the spaces CSbp and CSr of double series. Finally, we give the conditions which characterize the class of four-dimensional matrix mappings defined on the spaces CSbp, CSr and CSp of double series.     

Some paranormed sequence spaces of non-absolute type derived by weighted mean

The sequence spaces ?_∞(p), c(p) and c₀(p) were introduced and studied by Maddox [I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philos. Soc. 64 (1968) 335-340]. In the present paper, the sequence spaces λ(u,v;p) of non-absolute type which are derived by the generalized weighted mean are defined and proved that the spaces λ(u,v;p) and λ(p) are linearly isomorphic, where λ denotes the one of the sequence spaces ?_∞, c or c₀. Besides this, the β- and γ-duals of the spaces λ(u,v;p) are computed and the basis of the spaces c₀(u,v;p) and c(u,v;p) is constructed. Additionally, it is established that the sequence space c₀(u,v) has AD property and given the f-dual of the space c₀(u,v;p). Finally, the matrix mappings from the sequence spaces λ(u,v;p) to the sequence space μ and from the sequence space μ to the sequence spaces λ(u,v;p) are characterized.     

Hausdorff measure of noncompactness of certain matrix operators on the sequence spaces of generalized means

In the present paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence spaces of generalized means. Further, by applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for such operators to be compact.     

Necessary and sufficient conditions for the boundedness of B-Riesz potential in the B-Morrey spaces

We consider the generalized shift operator, associated with the Laplace-Bessel differential operator . The maximal operator Mγ (B-maximal operator) and the Riesz potential (B-Riesz potential), associated with the generalized shift operator are investigated. At first, we prove that the B-maximal operator Mγ is bounded from the B-Morrey space Lp,λ,γ to Lp,λ,γ for all 1<p<∞ and 0?λ<n+|γ|. We prove that the B-Riesz potential , 0<α<n+|γ| is bounded from the B-Morrey space Lp,λ,γ to Lq,λ,γ if and only if α/(n+|γ|−λ)=1/p−1/q, 1<p<(n+|γ|−λ)/α. Also we prove that the B-Riesz potential is bounded from the B-Morrey space L1,λ,γ to the weak B-Morrey space WLq,λ,γ if and only if α/(n+|γ|−λ)=1−1/q.     

Growth conditions, compact perturbations and operator subdecomposability, with applications to generalized Cesàro operators

We adapt recent results of Albrecht and Ricker to obtain conditions under which growth constraints on the left resolvent of a Banach space operator are preserved under suitable perturbations. As an application, we establish Bishop's property (β) for certain generalized Cesàro operators on the classical Hardy spaces Hp, 1<p<∞. Our methods also apply to unilateral weighted shifts whose weight sequence converges sufficiently rapidly as well as to perturbations of restrictions of a class of generalized scalar operators.     

Necessary and sufficient conditions for the boundedness of rough B-fractional integral operators in the Lorentz spaces

In this paper, the necessary and sufficient conditions are found for the boundedness of the rough B-fractional integral operators from the Lorentz spaces Lp,s,γ to Lq,r,γ, 1<p<q<∞, 1?r?s?∞, and from L1,r,γ to Lq,∞,γ≡WLq,γ, 1<q<∞, 1?r?∞. As a consequence of this, the same results are given for the fractional B-maximal operator and B-Riesz potential.     

Examples of non-archimedean Fréchet spaces without nuclear Köthe quotients

Let K be a spherically complete non-archimedean valued field. We prove that the dual space l_∞ of the Banach space c₀ has a total strongly non-norming subspace M. Using this subspace M we construct a non-normable Fréchet space F of countable type with a continuous norm such that its strong dual is a strict LB-space. Next we show that F has no nuclear Köthe quotient.     

Boundedness of dyadic derivative and Cesáro mean operator on some B-valued martingale spaces

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Cesàro mean operator σ* are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space.