Study On Chaotic Spectrum Of Operators

As an important concept of operator theory,spectral theory is of great value and significance.In this thesis,the definition of Li-Yorke chaos,distributionally chaos,Devaney chaos and the special relationship between these three types of chaos are first introduced.Then,we define the chaotic spectrum and study the differences between the properties of chaotic spectrum and classical spectrum.It is known that the spectrum of a bounded linear operator is a non-empty bounded closed set.We will obtain that the chaotic spectrum maintains the boundedness of the spectrum.However,the two properties of non-empty and bounded are no longer preserved,i.e.,there exists a bounded linear operator T such that the chaotic spectrum of T is either a null set or a non-closed set.