On the Generalizations and Properties of Abramovich-Wickstead Spaces

The present monograph concerns with new types of Abramovich-Wickstead spaces,the elements of which are the sums of real-valued (or vector valued in general) continuous functions and discrete functions on a compact Hausdorff space without isolated points, and analytic representations of different classes of dominated operators on these spaces. Although it is primarily based on the Ph.D. thesis of the author, the monograph provides further results and information on recent advances about that topic. The notion of a dominated operator was invented in the 1930s by L. V. Kantorovich. The idea of dominated operator can be stated as follows: if an operator under consideration is dominated by another operator, called a dominant, then the properties of the latter have a substantail influence on the properties of the former. Thus, operators that have nice dominants must posses nice properties. In this book, we are interested in giving some results concerning Banach space valued dominated operators on Abramovich-Wickstead spaces.