Karakterizacija ograničenih linearnih i kompaktnih operatora izmedju BK prostora

Abstract

Within this thesis , the new sequence spaces are introduced and the similarities and the differences between the matrix transformations and the general linear bounded operators on BK spaces are considered. The characterization of matrix transformations between new-defined sequence spaces is done by applying the theory of FK and BK spaces along with the results related to matrix domains of triangles. In some cases, where it is possible, the representation of general linear bounded operator is given by infinite matrix. Further on, the condition for compactness of certain classes of operators are given. Applying the Hausdorff measure of noncompactness, the necessary and sufficient conditions for compactness are obtained. In the cases where it is not possible, and where instead of the exact value we can only get the estimations for the measure of noncompactness of the operator, the results of Sargent are applied. This thesis contains some of such, improved, examples but also the new results concerning the newly defined spaces. The cases in which one can not apply the Hausdorff measure, nor the results of Sargent, are examined too, and the special properties of considered sequence spaces are used to obtain the characterizations of compact operators. In certain situations the results of compactness are formulated for the general bounded linear operators as well as for the matrix linear operators.