This book concerns with the theory of stable perturbations of operators in

Banach spaces . Thus the perturbation analysis for generalized inverses, the

Moore-Penrose inverse and Drazin inverse of operators under stable pertur-

bation. After a preliminary chapter including several basic results in Func-

tional Analysis ( Hilbert spaces, operators and C + algebras ) the book studies

carefully the relationships among the densely-defined operators with closed

range and the reduced minimum modulus of densely defined operators . The

Moore-Penrose inverse and its stable perturbations in Hilbert spaces and in

C ∗ -algebras is also presented . Several results of the K-theory in C + algebras

are also included. The last chapters of the book contain some miscellaneous

applications and related topics to the perturbation theory, like the approxi-

mate polar decomposition in C ∗ -algebras, and some applications of Moore-

Penrose inverses in frame theory.The list of references in the Bibliography is

quite extensive.

Reviewer:

Francisco L. Hernandez

Affiliation:

Universidad complutense de Madrid