Operator Theory on Noncommutative Domains.

Intro -- Contents -- Abstract -- Introduction -- Chapter 1. Operator algebras associated with noncommutative domains -- 1.1. The noncommutative domain Df and a universal model -- 1.2. The domain algebra An(Df) and its representations -- 1.3. The Hardy algebra Fn(Df) -- 1.4. Functional calculus for n-tuples of operators in Df -- 1.5. The noncommutative variety Vf,J and a functional calculus -- 1.6. Weighted shifts, symmetric weighted Fock spaces, and multipliers -- Chapter 2. Free holomorphic functions on noncommutative domains -- 2.1. Free holomorphic functions and Poisson transforms -- 2.2. Schwarz lemma and Bohr's inequality for Fn(Df) -- 2.3. Weierstrass and Montel theorems for the algebra Hol(Df) -- 2.4. Cauchy transforms and analytic functional calculus for n-tuples of operators -- Chapter 3. Model theory and unitary invariants on noncommutative domains -- 3.1. Weighted shifts and invariant subspaces -- 3.2. C*-algebras associated with noncommutative varieties and Wold decompositions -- 3.3. Dilations on noncommutative domains and varieties -- 3.4. Characteristic functions and model theory -- 3.5. Curvature invariant for n-tuples of operators in Dp -- Chapter 4. Commutant lifting and applications -- 4.1. Interpolation on noncommutative domains -- 4.2. Corona theorem for a class of Hardy algebras -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.