Wold Decompositions for Representations of C-Algebras Associated with Noncommutative Varieties

Explore the mathematical concepts of Wold decompositions for representations of C∗-algebras associated with noncommutative varieties in this 53-minute lecture by Gelu Popescu from the University of Texas at San Antonio. Delve into topics such as noncommutative domains, multivariable commutative and noncommutative cases, Berezin kernels, and various versions of Wold decomposition. Gain insights into the uniqueness of Wold decomposition, classification, exact sequences of C-algebras, and the relationship between polydomains and varieties. This talk, part of the Focus Program on Analytic Function Spaces and their Applications, offers a comprehensive overview of advanced mathematical concepts in functional analysis and operator theory.

Intro
Wold decomposition, 1954
Noncommutative domains
Noncommutative varieties (H)
Multivariable commutative case : 1 2
Multivariable noncommutative case
Noncommutative Berezin kernel
Constrained Berezin kernel
Wold decomposition : C-version
Wold decomposition : geometric version
Wold decomposition: operator version
Uniqueness of Wold decomposition
Classification
Exact sequences of C-algebras
Polydomains and varieties