This paper presents one theoretical ground and some simple applications of the mathematical tools applied to XML-based technologies, analyzed in the paper. The paper studies XML hierarchical constructions as structures of unranked trees, which lead to modern logical formalisms for querying and navigation over XML documents. By using some advanced algebraic tools, it is possible to work with ordinary linear operators for further data representation on the physical level instead of performing more difficult operations, which are specific for the widely used models. The realizations of the presented algebraic method implemented to real XML hierarchical data structures are connected with possibilities for high efficiency with respect to optimization of the time access to XML information. Some problems in the area of this specific XML terminology are discussed as well.