In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on thei...In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on their spaces of representations.We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls.We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.展开更多
基金supported by a grant from the U.S.-Israel Binational Science Foundation (Grant No. 200641)supported by the Technion V.P.R. Fund
文摘In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on their spaces of representations.We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls.We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.
