Noncommutative Function-Theoretic Operator Theory and Applications

Joseph A. Ball is Professor Emeritus at Virginia Tech in Blacksburg, Virginia. He won Virginia Tech's Alumni Award for Research Excellence in 1997 and is a member of the 2019 class of Fellows of the American Mathematical Society. He is co-author of Interpolation of Rational Matrix Functions (1990). Vladimir Bolotnikov is Professor of Mathematics at William & Mary in Williamsburg, Virginia. He has published over a hundred papers in operator and function theory.

• 1. Introduction; 2. Formal Reproducing Kenel Hilbert Spaces; 3. Contractive multipliers; 4. Stein relations and observability range spaces; 5. Beurling-Lax theorems based on contractive multipliers; 6. Non-orthogonal Beurling-Lax representations; 7. Orthogonal Beurling-Lax representations; 8. Models for ω-hypercontractive operator tuples; 9. Regular formal power series.

'Noncommutative Function-Theoretic Operator Theory and Applications by Ball and Bolotnikov is a comprehensive monograph by acknowledged experts in the fields of operator theory and function theory. It gives an account of a very active area of modern research, to which the authors themselves have been major contributors. The significant themes of the book include reproducing kernel Hilbert spaces (notably weighted Bergman spaces), Beurling-Lax theorems, and systems-theoretic ideas expressed in operator-theoretic terms. The work as a whole is presented in a multivariable noncommutative context, and thus extends classical work on Hardy-space function theory and related operator theory.' Jonathan Partington, University of Leeds