© 2017
Algebraic Properties of Generalized Inverses
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Part of the Developments in Mathematics book series (DEVM, volume 52)
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© 2017
Part of the Developments in Mathematics book series (DEVM, volume 52)
This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses.
Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse.
In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.
“The presentation is very clear. The proofs are described in detail. Another beautiful feature of this book is that each chapter ends with references. … Graduate students, Ph.D. students and researchers working on the theory of generalized inverses or closely related fields will benefit from this book.” (Debasisha Mishra, Mathematical Reviews, May, 2018)