Удк 517.98 Linear Operators on Abramovich–wickstead Type Space

CD0-type spaces were firstly introduced by Yu. A. Abramovich and A. W. Wickstead in [1] and [2] and further investigated by S. Alpay and Z. Ercan in [3]. CD0-type spaces deserve to be called Abramovich–Wickstead spaces, or briefly AW -space as in [4], since they mainly stem from the works of Yu. A. Abramovich and A. W. Wickstead. In this note we construct a new type AW -space and call it CDr 0 for the sake of convenience. Throughout this note, the symbols Lr and Ln denote the space of regular and order continuous regular operators respectively. For unexplained terminology about vector lattice theory, we refer to [5]. The first section is devoted to some introductory knowledge about vector-valued measures. This section will be useful in obtaining main results. For more detailed information about vector-valued measures, we refer to [6]. The second section of this note contains the definition of CDr 0-spaces. The third section is devoted to description of regular operators charactreziations about linear operators on CDr 0-space by means of vector measures and order summation. The fourth section contains two main results of the paper. In this section we are mainly interested in regular and order continuous regular operators on CDr 0-space with values in Dedekind complete vector lattices.