ESSENTIAL APPROXIMATE POINT AND ESSENTIAL DEFECT SPECTRUM OF A SEQUENCE OF LINEAR OPERATORS IN BANACH SPACES

摘要

This paper is devoted to an investigation of the relationship between the essential approximate point spectrum (respectively, the essential defect spectrum) of a sequence of closed linear operators (T_n)_(n?N) on a Banach space X, and the essential approximate point spectrum (respectively, the essential defect spectrum) of a linear operator T on X, where (T_n)_(n?N) converges to T, in the case of convergence in generalized sense as well as in the case of the convergence compactly.