Supercyclic Subspaces And Hypercyclic Subspaces On Banach Spaces

The paper studies about conditions for the existence of Supercyclic subspace onBanach space, and investigates the relationship between the Supercyclic operator on theSeparable Banach space and the left multiplication mapping in the Supercyclicity fromthe Supercyclicity criterion, and get the conclusion: when the operator satisfies somecertain conditions, a Supercyclic vector on the left multiplication mapping combineswith nonzero element that can be a Supercyclic vector of the operator; starting fromthe Supercyclic vector, it can construct Supercyclic subspace of the operator, and thenget the sufficient condition of the existence of Supercyclic subspace. Further givessufficient conditions for the existence of Supercyclic subspace of infinite straight-sumof operator.The paper is arranged as follows:The first chapter mainly introduces the definitions, examples and conclusions ofCyclic operator, Supercyclic operator, and Hypercyclic operator.The second chapter mainly introduces the related concepts, theorems, examples,properties and main conclusions of Hypercyclic space and Supercyclic space.The third chapter, on one hand, introduces how to determine whetherHypercyclic operator has Hypercyclic subspace on Banach space and giventhe existing conditions of Hyercyclic space; on the other hand, discussed therelationship between the Supercyclic operator on the Separable Banach space and theleft multiplication mapping in the Supercyclicity from the Supercyclicity criterion, andget the conclusion: when the operator satisfies some certain conditions, aSupercyclic vector on the left multiplication mapping combines with nonzero elementthat can be a Supercyclic vector of the operator; and discussed the Supercyclicsubspace of the Supercyclic operator, and a sufficient condition for the existence ofSupercyclic subspace is given.The fourth chapter, this paper sums up the whole thesis based on the paper, and abrief introduction to the problem of later research.