Properties Of Supercyclic Operator And Subspace-supercyclic Operators

The paper systematically introduces the concept of Hypercyclic operators, Supercyclic operators and Subspace- hypercyclic operators, and it also gives some examples and basic conclusion of these operators.We compare the property of Hypercyclic operators with Supercyclic operators, and according to the basis of Hypercylic operators, we study related properties of Superc yclic operators and Subspace-supercyclic operator. In this thesis, we mainly get the following conclusions:On the one hand, three sufficient condition for a bounded linear operator to be Supercyclic are obtained. O ne of the theorems tell us: knowning a re versible Supercyclic operator, then we will be able to construct a series of Supercyclic operator; another one theorem mainly makes use of d- dense of orbit C×Orb(x,T), its proof is more value than this theorem itself, knowledge utilization is relatively abundant, and can be used to prove a similar theorem. The third sufficient condition is given by the operator’s invariant closed subset.On the other hand, we research Subsapce-supercyclicity of shift operators and weighted shift operators. Shift operators is a kind of common cycle operator, it plays an very important role on operator theory. By Subspace-hypercyclic operator inspired research on shift operators, Subspace-supercyclic operator decision theorem is given.At last, we consider reversible Supercyclic operator, and charcacterize the Supercyclicity of T and 1T- from the perspective of the Supercyclic vector.Finally, give a summary of the full text, and the prospect of issues still need to continue research.