Dilation and Model Theory for Pairs of Commuting Contraction Operators

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.

Author: Joseph A. Ball,Haripada Sau
Binding Type: Hardcover
Publisher: Cambridge University Press
Published: 07/23/2026
Series: Cambridge Tracts in Mathematics #236
Pages: 316
Weight: 1.3lbs
Size: 9.00h x 6.00w x 0.75d
ISBN: 9781009687218