Eigenvalue Problem Of Anti-triangular Operator Matrices~1

This thesis is concerned with the eigenvalue problem of anti-triangular operator ma-trices in a Hilbert space.For,it is shown that the algebraic index of eigenvalues are 1 and their eigenvector systems are of orthogonality,based on the properties of their operator entries.Furthermore,necessary and sufficient conditions are given for their eigenvector system to be complete in the sense of Cauchy principal value.Finally,we present some examples to illustrate the effectiveness of the results.