Dilation and Model Theory for Pairs of Commuting Contraction Operators
Book Details
Format
Hardback or Cased Book
Book Series
Cambridge Tracts in Mathematics
ISBN-10
1009687212
ISBN-13
9781009687218
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jul 23rd, 2026
Print length
316 Pages
Weight
574 grams
Dimensions
23.50 x 16.10 x 2.40 cms
Product Classification:
AlgebraFunctional analysis & transformsFunctional analysis and transforms
Ksh 21,050.00
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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.
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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