The sequence space bv and some applications

In this work, we give well-known results related to some properties, dual spaces and matrix transformations of the sequence space bv and introduce the matrix domain of space bv with arbitrary triangle matrix A. Afterward, we choose the matrix A as Ces\`aro mean of order one, generalized weighted mean and Riesz mean and compute alpha-; beta- gamma-duals of these spaces. And also, we characterize the matrix classes of the new spaces.Comment: 9 page

Conditioned square functions for noncommutative martingales

We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative $L^p$-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948--995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.Comment: Published at http://dx.doi.org/10.1214/009117906000000656 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Method of almost convergence with operator of the form fractional order and applications

The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those concepts are presented. Second, we construct the almost convergent spaces with fractional order difference operator and compute dual spaces which are help us in the characterization of matrix mappings. After we characterize to the matrix transformations, we give some examples.Comment: 20 pages, 4 table