ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

摘要

Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps on B(X)preserving Fredholm operators with fixed nullity or defect equal to n in both directions,and describe completely the structure of these maps.