Resumen de Perturbations of operators satisfying a local growth condition

B. P. Duggal

• A Banach space operator T 2 B(X) satis¯es a local growth condition of order m for some positive integer m , T 2 loc(Gm), if for every closed subset F of the set of complex numbers and every x in the glocal spectral subspace XT (F) there exists an analytic function f : CnF ! X such that (T ¡¸)f(¸) ´ x and jjf(¸)jj · K[dist(¸; F)]¡mjjxjj for some K > 0 (independent of F and x). Browder-Weyl type theorems are proved for perturbations by an algebraic operator of operators which are either loc(Gm) or polynomially loc(Gm).