Dilation and Model Theory for Pairs of Commuting Contraction Operators (Cambridge Tracts in Mathematics) - Hardcover

Ball, Joseph A.; Sau, Haripada

Hardcover

ISBN 10: 1009687212 ISBN 13: 9781009687218

Publisher: Cambridge University Press, 2026

Synopsis

Exactly a decade after the publication of the Sz.-Nagy Dilation Theorem, Tsuyoshi Andō 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 Andō'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 Andō's first step comes this thorough systematic treatment of a dilation and model theory for pairs of commuting contractions.

About this title

About the Authors

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2026
• Language: English
• ISBN 10: 1009687212
• ISBN 13: 9781009687218
• Binding: Hardcover
• Number of pages: 314