Dilation and Model Theory for Pairs of Commuting Contraction Operators

By: Joseph A. Ball, Haripada Sau

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Hardcover | 23 July 2026

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Hardcover
316 Pages

Dimensions(cm)
23.5 x 16.1 x 2.4

Hardcover

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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.-Nagyâ"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.

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