Abstract
Let T be a bounded linear operator on a Banach space X, and let M be a closed T-invariant subspace of X. In this paper, we investigate the relationships between the essential spectrum and the Browder spectrum of T, and those of the operators T-M and (T-M) over bar, where T-M is the restriction of T to M, and (T-M) over bar is the operator induced by T on the quotient space X/M.