**Mathematical Surveys and Monographs**

Volume: 267;
2022;
170 pp;
Softcover

MSC: Primary 47; 15;

**Print ISBN: 978-1-4704-6987-0
Product Code: SURV/267**

List Price: $125.00

AMS Member Price: $100.00

MAA Member Price: $112.50

**Electronic ISBN: 978-1-4704-7113-2
Product Code: SURV/267.E**

List Price: $125.00

AMS Member Price: $100.00

MAA Member Price: $112.50

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#### Supplemental Materials

# Completion Problems on Operator Matrices

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*Dragana S. Cvetković Ilić*

Completion problems for operator matrices are
concerned with the question of whether a partially specified operator
matrix can be completed to form an operator of a desired type. The
research devoted to this topic provides an excellent means to
investigate the structure of operators. This book provides an
overview of completion problems dealing with completions to different
types of operators and can be considered as a natural extension of
classical results concerned with matrix completions.

The book assumes some basic familiarity with functional analysis
and operator theory. It will be useful for graduate students and
researchers interested in operator theory and the problem of matrix
completions.

#### Readership

Graduate students and researchers interested in functional analysis, operator matrices, and operator theory.

#### Table of Contents

# Table of Contents

## Completion Problems on Operator Matrices

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Notation xi12
- Chapter 1. Completion problems for upper triangular operator matrices 116
- 1.1. Completions of upper triangular operator matrices to injective and left invertible operator 217
- 1.2. Completions of upper triangular operator matrices to invertible and right invertible operator 722
- 1.3. Completions of upper triangular operator matrices to regular operator 1328
- 1.4. Completions of upper triangular operator matrices to Drazin and generalized Drazin invertible operator 1934
- 1.5. Completions of upper triangular operator matrices to Fredholm operator 2843
- 1.6. Completions of upper triangular operator matrices to generalized left and right Weyl operator 3651
- 1.7. Completions of upper triangular operator matrices to Browder operator 4459
- 1.8. Completions of upper triangular matrices to Kato nonsingular operator 5267
- 1.9. Fredholm consistency of upper triangular operator matrices 6378

- Chapter 2. Invertibility of an operator 𝐴+𝐶𝑋 7590
- 2.1. Auxiliary results 7590
- 2.2. Invertibility of an operator 𝐴+𝐶𝑋 7792
- 2.3. Injectivity of an operator 𝐴+𝐶𝑋 8196
- 2.4. Surjectivity of an operator 𝐴+𝐶𝑋 8499
- 2.5. Right and left invertibility of an operator 𝐴+𝐶𝑋 86101
- 2.6. Fredholmness of an operator 𝐴+𝐶𝑋 88103
- 2.7. Dense range of an operator 𝐴+𝐶𝑋 93108
- 2.8. Closed range of an operator 𝐴+𝐶𝑋 95110

- Chapter 3. Completions of operator matrices 𝑀_{𝑋} 101116
- 3.1. Completions of operator matrices 𝑀_{𝑋} to invertible operator 102117
- 3.2. Completions of 𝑀_{𝑋} to injective and nondense range operator 107122
- 3.3. Completions of operator matrices 𝑀_{𝑋} to right and left invertible operator 113128
- 3.4. Completions of operator matrices 𝑀_{𝑋} to semi-Fredholm operator 115130
- 3.5. Completions of operator matrices 𝑀_{𝑋} to Fredholm operator 120135
- 3.6. Completions of operator matrices 𝑀_{𝑋} to closed range operator 122137

- Chapter 4. Completions of operator matrices 𝑀_{(𝑋,𝑌)} 125140
- Chapter 5. Applications of completion results 139154
- Bibliography 159174
- Index 169184
- Back Cover Back Cover1187