Dilation and Model Theory for Pairs of Commuting Contraction Operators

By Joseph A. Ball and Haripada Sau

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

• Format: Hardcover
• Language: English
• ISBN: 1009687212
• ISBN13: 9781009687218
• Release Date: July 2026
• Publisher: Cambridge University Press
• Length: 314 Pages