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.     

Δ-Strongly summable sequences spaces in 2-normed spaces defined by ideal convergence and an Orlicz function

In this paper, we study certain new difference sequence spaces using ideal convergence and an Orlicz function in 2-normed spaces and we give some relations related to these sequence spaces.     

赋范线性空间中的列收敛

本文证明了Ｓｃｈｕｒ空间与有限维Ｂａｎａｃｈ空间的两个特征定理，并对赋范线性空间中的列收敛进行了讨论，得到了一些有趣的结果。     

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),?_∞).     

Dual pairs of sequence spaces. III

In the previous papers [J. Boos, T. Leiger, Dual pairs of sequence spaces, Int. J. Math. Math. Sci. 28 (2001) 9-23; J. Boos, T. Leiger, Dual pairs of sequence spaces. II, Proc. Estonian Acad. Sci. Phys. Math. 51 (2002) 3-17], the authors defined and investigated dual pairs (E,ES), where E is a sequence space, S is a BK-space on which a sum s is defined in the sense of Ruckle [W.H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, 1981], and ES is the space of all factor sequences from E into S. In generalization of the SAK-property (weak sectional convergence) in the case of the dual pair (E,Eβ), the SK-property was introduced and studied. In this note we consider factor sequence spaces E|S|, where |S| is the linear span of , the closure of the unit ball of S in the FK-space ω of all scalar sequences. An FK-space E such that E|S| includes the f-dual Ef is said to have the SB-property. Our aim is to demonstrate, that in the duality (E,ES), the SB-property plays the same role as the AB-property in the case ES=Eβ. In particular, we show for FK-spaces, in which the subspace of all finitely non-zero sequences is dense, that the SB-property implies the SK-property. Moreover, in the context of the SB-property, a generalization of the well-known factorization theorem due to Garling [D.J.H. Garling, On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967) 997-1019] is given.     

Saturating constructions for normed spaces II

We prove several results of the following type: given finite-dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) and (2) every subspace of X, whose dimension is not “too small”, contains a further well-complemented subspace nearly isometric to V. This sheds new light on the structure of large subspaces or quotients of normed spaces (resp., large sections or linear images of convex bodies) and provides definitive solutions to several problems stated in the 1980s by Milman.     

Pointwise lineability in sequence spaces

We continue the research on lineability/spaceability properties in sequence spaces. Our main results show that several theorems in this framework are valid in a stricter sense. To do this job we introduce the notion of pointwise lineability which seems to be of independent interest for further investigations in other environments.     

Generalized vector-valued paranormed sequence space using modulus function

In this paper we introduce a generalized vector-valued paranormed sequence space N_p(E_k,Δ^m,f,s) using modulus function f, where p=(p_k) is a bounded sequence of positive real numbers such that inf_kp_k>0,(E_k,q_k) is a sequence of seminormed spaces with E_k+1⊆E_k for each k ∈ N and s?0. We have also studied sequence space N_p(E_k,Δ^m,f^r,s), where f^r=f°f°f°,…,f (r-times composition of f with itself) and r∈N={1,2,3,…}. Results regarding completeness, K-space, normality, inclusion relations etc. are derived. Further, a study of multiplier of the set N_p(E_k,f,s) is also made by choosing (E_k,‖·‖_k) as sequence of normed algebras.     

-Difference sequence spaces of fuzzy numbers

In this paper, using the difference operator of order m and an Orlicz function, we introduce and examine some classes of sequences of fuzzy numbers. We give the relations between the strongly Cesàro type convergence and statistical convergence in these spaces. Furthermore, we study some of their properties like completeness, solidity, symmetricity, etc. We also give some inclusion relations related to these classes.     

Weakly convergent sequence coefficient in Köthe sequence spaces

In this paper, we have discussed the weakly convergent sequence coefficient in Köthe sequence spaces with as their boundedly complete basis. Using those results, we can easily calculate the weakly convergent sequence coefficient in Orlicz sequence spaces.

     

Complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm

In this paper, two equivalent definitions of complex strongly extreme points in general complex Banach spaces are shown. It is proved that for any Orlicz sequence space equipped with the p-Amemiya norm (1?p<∞, p is odd), complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in Orlicz sequence spaces equipped with the p-Amemiya norm are given. Criteria for complex mid-point locally uniform rotundity and complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm are also deduced.     

Existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature

We prove that if for the curved n-body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero. We furthermore prove that the set of all such relative equilibria is compact. This class of relative equilibria includes all relative equilibria of the curved n  -body problem in H²${\mathbb{H}}^2$ and a significant subset of the relative equilibria for S²${\mathbb{S}}^2$, S³${\mathbb{S}}^3$ and H³${\mathbb{H}}^3$.     

Weighted differentiation composition operators from H and Bloch spaces to nth weighted-type spaces on the unit disk

We characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions, the Bloch space and the little Bloch space to nth weighted-type spaces on the unit disk.     

On ideal convergence of double sequences in probabilistic normed spaces

The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general.     

Hahn-Banach theorems in nonstandard normed interval spaces

The conventional Hahn-Banach extension theorem based on vector space has been widely used to obtain many important and interesting results in nonlinear analysis, vector optimization and mathematical economics. Although the interval space is not a real vector space, the Hahn-Banach extension theorems based on interval spaces and nonstandard normed interval spaces can still be derived in this paper, which also shows the possible applications by considering the interval-valued problems in nonlinear analysis, vector optimization and mathematical economics.     

Finitary sequence spaces

This paper studies the metric structure of the space H_r of absolutely summable sequences of real numbers with at most r nonzero terms. H_r is complete, and is located and nowhere dense in the space of all absolutely summable sequences. Totally bounded and compact subspaces of H_r are characterized, and large classes of located, totally bounded, compact, and locally compact subspaces are constructed. The methods used are constructive in the strict sense. MSC: 03F65, 54E50.     

Some new generalized difference sequence spaces defined by a sequence of moduli

The idea of difference sequence sets X( ) = {x = (x k ) : x ∈ X} with X = l ∞ , c and c 0 was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations.     

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.     

James orthogonality and orthogonal decompositions of Banach spaces

We establish decompositions of a uniformly convex and uniformly smooth Banach space B and dual space B^∗ in the form B=M?J^∗M^⊥ and B^∗=M^⊥?JM, where M is an arbitrary subspace in B, M^⊥ is its annihilator (subspace) in B^∗, J:B→B^∗ and J^∗:B^∗→B are normalized duality mappings. The sign ? denotes the James orthogonal summation (in fact, it is the direct sums of the corresponding subspaces and manifolds). In a Hilbert space H, these representations coincide with the classical decomposition in a shape of direct sum of the subspace M and its orthogonal complement M^⊥: H=M⊕M^⊥.