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Algebraic Properties of Generalized Inverses

  • Dragana S. Cvetković‐Ilić
  • Yimin Wei

Part of the Developments in Mathematics book series (DEVM, volume 52)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 1-10
  3. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 11-50
  4. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 51-88
  5. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 89-108
  6. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 109-158
  7. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 159-192
  8. Back Matter
    Pages 193-194

About this book

Introduction

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.

Keywords

Drazin inverse idempotent generalized and hypergeneralized Reverse order law Operators on Banach spaces Moore-Penrose inverse

Authors and affiliations

  • Dragana S. Cvetković‐Ilić
    • 1
  • Yimin Wei
    • 2
  1. 1.Faculty of Science and MathematicsUniversity of NisNisSerbia
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-6349-7
  • Copyright Information Springer Nature Singapore Pte Ltd. 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-10-6348-0
  • Online ISBN 978-981-10-6349-7
  • Series Print ISSN 1389-2177
  • Series Online ISSN 2197-795X
  • Buy this book on publisher's site