Theoretical Research On Generalized Operators C-Semigroup And Generalized Operators C-Group

In this thesis, firstly, on the basis of existing studied in generalized operator C₀- semigroups and generalized operator C-semigroups, generalized operator C-semigroups generated theorem, perturbation theorem and spectral mapping theorem are got. Secondly, fully continuous generalized operator C-semigroups concept and fully continuous generalized operator C-semigroups related properties are studied. Finally, it gives the definition of the generalized operator C-groups, and discusses the relationship of generalized operator C-groups and generalized operator C-semigroups. The full thesis is divided into four parts:The first part, according to the definition, generator and nature of generalized operator C-semigroups, generalized operator C-semigroups generated theorem, perturbation theorem are researched. What conditions does linear operator A satisfy, it can generate generalized operator C-semigroups. If B is a bounded linear operator on a banach space, then A + B is another generalized operator C-semigroups’ generator;The second part, C spectrum of generalized operator C-semigroups is defined, and some properties of the spectrum are researched. Finally, a generalized operator C-semigroups spectral mapping theorem is got;The third part, according to the definition of generalized operator C-semigroups and fully continuous generalized operator C₀-semigroups, fully continuous generalized operator C-semigroups and the generator are defined, fully continuous generalized operator C-semigroups some properties, and the nature of generators of fully continuous generalized operator C-semigroups are studied;The fourth part, the definition of generalized operator C-groups and generators are gaven. the relationship between generalized operator C-groups and generalized operator C-semigroups is discussed by using classical operators theory. A and-A is represented generator of two generalized operator C-semigroups, it came to the conclusion that A is the generalized operator C-groups generator.