We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diago...We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).展开更多
The authors extend Hua’s fundamental theorem of the geometry of Hermitian matri- ces to the in?nite-dimensional case. An application to characterizing the corresponding Jordan ring automorphism is also presented.
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 National Natural Science Foundation of China(Grant No.11371290)
文摘We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).
基金Project supported by the National Natural Science Foundation of China (No.10471082) and the ShanxiProvincial Natural Science Foundation of China.
文摘The authors extend Hua’s fundamental theorem of the geometry of Hermitian matri- ces to the in?nite-dimensional case. An application to characterizing the corresponding Jordan ring automorphism is also presented.
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.
