Dilation and Model Theory for Pairs of Commuting Contraction Operators

Erscheinungsjahr 2026
ISBN: 978-1-009-68721-8
Verlag: Cambridge University Press

Buch, Englisch, Band 236, 316 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 610 g

Reihe: Cambridge Tracts in Mathematics

Exactly a decade after the publication of the Sz.-Nagy dilation theorem, Tsuyoshi Ando proved that, just like for a single contractive operator, every commuting pair of Hilbert-space contractions can be lifted to a commuting isometric pair. Although the inspiration for Ando's proof comes from the elegant construction of Schäffer for the single-variable case, his proof did not shed much light on the explicit nature of the dilation operators and the dilation space as did the original Schäffer and Douglas constructions for a single contraction. Consequently, there has been little follow-up in the direction of a more systematic extension of the Sz.-Nagy–Foias dilation and model theory to the bivariate setting. Sixty years since the appearance of Ando's first step comes this thorough systematic treatment of a dilation and model theory for pairs of commuting contractions.

Autoren/Hrsg.

Ball, Joseph A.

Sau, Haripada

Inhaltsverzeichnis

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. Ando's dilation and commutant lifting theorems; 5. Douglas-type model for Ando isometric lifts; 6. Schäffer-type model for Ando isometric lifts; 7. Strongly minimal Ando 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.

Über Autor(innen)

Ball, Joseph A.
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.

Sau, Haripada
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.