Stability of index for linear relations and its applications

This paper is concerned with the stability of linear relations in Banach and Hilbert spaces. Several important results about the stability of closedness and the stability of indices of operators in Banach spaces are extended to the linear relations in Banach spaces. Moreover, the stability of deficiency indices of dissipative linear relations in Hilbert spaces is studied. As an important application, we discuss the stability of deficiency indices of dissipative linear relations generated by second-order difference expressions.