Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 31 num. 2 lang. en <![CDATA[SciELO Logo]]> <![CDATA[Asymptotically convex Banach spaces and The Index of Rotundity Problem]]> The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: asymptotically convex Banach spaces. Some applications to The Approximation Hyperplane Series Property are given. <![CDATA[Polar topologies on sequence spaces in non-archimedean analysis]]> The purpose of the present paper is to develop a theory of a duality in sequence spaces over a non-archimedean vector space. We introduce polar topologies in such spaces, and we give basic results characterizing compact, C-compact, complete and AK -complete subsets related to these topologies. <![CDATA[<b>Some separation axioms in L-topological spaces</b>]]> In this paper, under the idea of L-Tq or sub-T0,we propose a set of new separation axioms in L-topological spaces, namely sub-separation axioms. And some of their properties are studied. In addition, the relation between the sub-separation axioms defined in the paper and other separation axioms is discussed. The results show that the sub-separation axioms in this paper are weaker than other separation axioms that had appeared in literature. <![CDATA[Uniform Convergence and the Hahn-Schur Theorem]]> Let E be a vector space, F aset, G be a locally convex space, b : E X F - G a map such that ò(-,y): E - G is linear for every y G F; we write b(x, y) = x · y for brevity. Let ë be a scalar sequence space and w(E,F) the weakest topology on E such that the linear maps b(-,y): E - G are continuous for all y G F .A series Xj in X is ë multiplier convergent with respect to w(E, F) if for each t = {tj} G ë ,the series Xj=! tj Xj is w(E,F) convergent in E. For multiplier spaces ë satisfying certain gliding hump properties we establish the following uniform convergence result: Suppose j XX ij is ë multiplier convergent with respect to w(E, F) for each i G N and for each t G ë the set {Xj=! tj Xj : i} is uniformly bounded on any subset B C F such that {x · y : y G B} is bounded for x G E.Then for each t G ë the series ^jjLi tj xj · y converge uniformly for y G B,i G N. This result is used to prove a Hahn-Schur Theorem for series such that lim¿ Xj=! tj xj · y exists for t G ë,y G F. Applications of these abstract results are given to spaces of linear operators, vector spaces in duality, spaces of continuous functions and spaces with Schauder bases. <![CDATA[<b>Hochschild-Serre</b><b> Statement for the total cohomology</b>]]> Let M be a complex manifold and F a Om-module with a g-holomorphic action where g is a complex Lie algebra (cf. [3]). We denote by H(g, F) the "total cohomology" as defined in [1] [2]. Then we prove that, for any ideal a c g,the module H* (a, F) viewed as a g/a-module, we have a spectral sequence which converges to H(g, F) <![CDATA[<b>Generalized difference entire sequence spaces</b>]]> In this paper we introduce difference entire sequence spaces and difference analytic sequence spaces defined by a sequence of modulus function F = (/¾) and study some topological properties and some inclusion relations between these spaces. We also make an effort to study some properties and inclusion relation between the spaces Tf(ÁÃ , u, p, q, ||., ···, .||) and Af(A^ , u, p, q, ||., ·· ·, .\\).