Dilation and Model Theory for Pairs of Commuting Contraction Operators

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Inbunden, Engelska, 2026

AvJoseph A. Ball,Haripada Sau,Joseph A Ball

1 919 kr

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Exactly a decade after the publication of the Sz.-Nagy Dilation Theorem, Tsuyoshi Andô 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 Andô'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 bi-variate setting. Sixty years since the appearance of Andô's first step comes this thorough systematic treatment of a dilation and model theory for pairs of commuting contractions.

Produktinformation

Utgivningsdatum2026-07-31
FormatInbunden
SpråkEngelska
SerieCambridge Tracts in Mathematics
Antal sidor314
FörlagCambridge University Press
ISBN9781009687218

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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.