Dilation and model theory for pairs of commuting contraction operators / Joseph A. Ball, Haripada Sau

Format:

Book

Author/Creator:

Ball, Joseph A., 1947- author.

Sau, Haripada, author.

Series:

Cambridge tracts in mathematics ; 236.

Cambridge tracts in mathematics ; 236

Language:

English

Subjects (All):

Contraction operators.

Dilation theory (Operator theory).

Physical Description:

1 online resource

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"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"-- Cambridge Core

This reference will be of interest to researchers working in multivariable operator theory. It is accessible to anyone with a first-year graduate-student-level background in analysis, in particular Hardy-space operator theory and functional analysis

Contents:

Models for unitary dilations and isometric lifts of a contraction operator

The Berger-Coburn-Lebow and Bercovici-Douglas-Foias models for pairs of commuting isometries

Ando’s dilation and commutant lifting theorems

Douglas-type model for Ando isometric lifts

Schäfer-type model for Ando isometric lifts

Strongly minimal Ando isometric lifts and fundamental operators

Pseudo-commuting contractive lifts

Functional model and invariants for commuting contractive pairs

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed July 24, 2026)

Other Format:

Print version: Ball, Joseph A., 1947- Dilation and model theory for pairs of commuting contraction operators

ISBN:

9781009687195

1009687190

9781009687225

1009687220

OCLC:

1594240714

Publisher Number:

CIPO000401480

Access Restriction:

Restricted for use by site license