We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented. It is a well-known result that a Banach space whose dual norm is Fréchet differentiable is reflexive. Also if the the third dual norm is Gâteaux differentiable the space is reflexive. For these results see e.g. [2], p.33. Similarly, by the result of [9], if the sec...

this paper examines the problematization of cultural issues related tothe dual spacization of life. the emergence of the second space of lifeover the first place of life combining local and translocal, national andtransnational capacities and challenges. we discuss the capacities andopportunities occurring through the instant communication industrywhich made the spontaneous connection between a...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

This paper examines the problematization of cultural issues related tothe dual spacization of life. The emergence of the second space of lifeover the first place of life combining local and translocal, national andtransnational capacities and challenges. We discuss the capacities andopportunities occurring through the instant communication industrywhich made the spontaneous connection between a...