Spectral Properties of Generalized Inverses of Linear Operators
David C. Lay · SIAM Journal on Applied Mathematics · 1975
Let A be a bounded linear operator on a Banach space, and suppose that A has a generalized inverse B. This paper investigates conditions under which the nonzero points in the spectrum of B are the reciprocals of the nonzero points in the spectrum of A. The concept of a spectral (generalized) inverse of a square matrix, introduced by T. N. E. Greville, is extended here to a bounded linear operator on a Banach space.