Abstract :
Let T and S be two bounded linear operators from Banach spaces X into Y,
and suppose that T is Fredholm and dim NŽT S.is constant in a neighborhood
of 0. Let dŽT; S.be the supremum of all r 0 such that dim NŽT S.and
codim RŽT S.are constant for all with r. It is a consequence of more
general results due to H. Bart and D. C. LayŽ1980, Studia Math. 66, 307 320.that
dŽT; S. lim n nŽT; S.1 n, where nŽT; S.are some non-negativeŽextended.
real numbers. For X Y and S I, the identity operator, we have nŽT; S.
ŽT n., where is the reduced minimum modulus. A different representation of
the stability radius dŽT; S.is obtained here in terms of the spectral radii of
generalized inverses of T. The existence of generalized resolvents for Fredholm
linear pencils is also considered.
