Dilation and Model Theory for Pairs of Commuting Contraction Operators
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- Publisher:
- Cambridge University Press
- Publication date:
- 26 June 2026
- 23 July 2026
- ISBN:
- 9781009687225
- 9781009687218
- Dimensions:
- (229 x 152 mm)
- Weight & Pages:
- 0.623kg, 316 Pages
- Dimensions:
- Weight & Pages:
- Subjects:
- Mathematics (general), Mathematics, Abstract Analysis
- Series:
- Cambridge Tracts in Mathematics (236)
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- Mathematics (general), Mathematics, Abstract Analysis
- Series:
- Cambridge Tracts in Mathematics (236)
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Book description
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.
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