Dilation and Model Theory for Pairs of Commuting Contraction Operators

Joseph A. Ball is Professor Emeritus at Virginia Tech, a fellow of the American Mathematical Society, and co-author of the books 'Interpolation of Rational Matrix Functions' (1990) and 'Noncommutative Function-Theoretic Operator Theory and Applications' (2022) as well as approximately 200 research articles in operator and mathematical systems theory. Haripada Sau is Assistant Professor at the Indian Institute of Science Education and Research Pune. He works at the interface of operator theory and holomorphic function theory. He was awarded the Young Associateship by the Indian Academy of Science and the Indian National Science Academy in recognition of his work on the rational dilation problem and certain affine varieties.

• Preface; 1. Introduction; 2. Models for unitary dilations and isometric lifts of a contraction operator; 3. The Berger–Coburn–Lebow and Bercovici–Douglas–Foias models for pairs of commuting isometries; 4. Andô's dilation and commutant lifting theorems; 5. Douglas-type model for Andô isometric lifts; 6. Schäffer-type model for Andô isometric lifts; 7. Strongly minimal Andô isometric lifts and fundamental operators; 8. Pseudo-commuting contractive lifts; 9. Functional model and invariants for commuting contractive pairs; Appendix. More general domains and open problems; References; Index.