To the spectral theory of operators in Hilbert space

In this book we give the sufficient conditions for the existence of the eigenvalues of completely continuous operators, polynomial bundles, multiparameter operator systems in Hilbert spaces.It is investigated the questions of existence of common eigenvalues and eigenvectors of two and more completely continuous operators, polynomial operator bundles. It is also studied the spectral properties of completely continuous oprators in Hilbert space.It's introduced the class of normal operators in Banach space. For them It is proved the main properties of normal operators, acting in Hilbert spaces.