Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Continuity of the generalized kernel and range of semi-Fredholm operators

M. Ó Searcóida1 and T. T. Westa2

a1 University College, Dublin

a2 Trinity College, Dublin

Let X denote a Banach space over the complex field ℂ and let B(X) be the Banach algebra of all bounded linear operators on X. If T ε B(X), we write n(T) = dim ker (T) and d(T) = codim T(X). Suppose that Y is a subspace invariant under T; then TY will denote the restriction of T to Y and S0305004100077896_inline1Y the operator on X/Y defined by

S0305004100077896_inline1Y: x/Y →(Tx)/Y

(Received May 02 1988)