| Abstract [eng] |
This Master's thesis consists of theoretical and practical parts. In the theoretical part of the work, the theoretical material of compact sets and compact operators in various spaces is presented. This material is considered in topological, metric and normed linear spaces. Some statements are valid only for complete metric spaces. The last chapter of the theoretical part proves the main spectral theorems of compact operators. The practical part of the Master's thesis illustrates the theoretical part with several solved problems: the Hilbert Schmidt operators are considered, their compactness and other results are proved, and the spectrum is found. The goal of this thesis is to present the concept of compactness in various spaces, review linear compact operators and their spectral theory. |
