The main result of this paper is the following: A separable Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence on nested, closed, finite codimensional subspaces with null intersection.
The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in -normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.
In this paper, following the methods of Connor [connor], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [moe]) to -statistical convergence and convergence in -density using a two valued measure . We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure called the (APO) condition, inspired by the (APO) condition of Connor [jc]. We mainly investigate...