From the reviews of the first edition: "The primary goal of this monograph is a presentation of the Fredholm and Riesz theory of Banach space operators and applications in the stetting of multipliers of a commutative Banach algebra. ... This book complements standard references for Fredholm theory ... on the one hand, and Laursen and Neumann's book on the other hand. It should prove to be a valuable resource for graduate students and researchers in Banach space operator theory." (Thomas Len Miller, Mathematical Reviews, 2005e) "The main concern of the monograph under review is Fredholm theory and its connections with the local spectral theory for bounded linear operators in Banach spaces. ... The monograph is intended for the use of researchers and graduate students in functional analysis, having a certain background in operator theory. The style is alert and pleasant and there is a fair and state-of-the-art account of the actual Fredholm theory in connection with local spectral theory." (Florian-Horia Vasilescu, Zentralblatt MATH,Vol. 1077 (3), 2006)

• The Kato decomposition property.- The single-valued extension property.- The SVEP and Fredholm theory.- Multipliers of commutative Banach algebras.- Abstract Fredholm theory.- Decomposability.- Perturbation classes of operators.

From the reviews of the first edition: "The primary goal of this monograph is a presentation of the Fredholm and Riesz theory of Banach space operators and applications in the stetting of multipliers of a commutative Banach algebra. ... This book complements standard references for Fredholm theory ... on the one hand, and Laursen and Neumann's book on the other hand. It should prove to be a valuable resource for graduate students and researchers in Banach space operator theory." (Thomas Len Miller, Mathematical Reviews, 2005e) "The main concern of the monograph under review is Fredholm theory and its connections with the local spectral theory for bounded linear operators in Banach spaces. ... The monograph is intended for the use of researchers and graduate students in functional analysis, having a certain background in operator theory. The style is alert and pleasant and there is a fair and state-of-the-art account of the actual Fredholm theory in connection with local spectral theory." (Florian-Horia Vasilescu, Zentralblatt MATH,Vol. 1077 (3), 2006)

• The Kato decomposition property.- The single-valued extension property.- The SVEP and Fredholm theory.- Multipliers of commutative Banach algebras.- Abstract Fredholm theory.- Decomposability.- Perturbation classes of operators.