Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive integer.We give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphism...Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive integer.We give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphismφ:A→Mn(B).We give an equivalent characterization of McDuff Ⅱ_(1) factors.We show that,if A is a unital nuclear C^(∗)-algebra and B is a type Ⅱ_(1) factor with faithful traceτ,then every unital^(∗)-homomorphism φ:A→M_(n)(B)is weakly approximately diagonalizable.If B is a unital simple infinite dimensional separable nuclear C^(∗)-algebra,then any finitely many elements in Mn(B)can be simultaneously weakly approximately diagonalized while the elements in the diagonals can be required to be the same.展开更多
Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity prop...Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.展开更多
基金supported by the Natural Science Foundation of Chongqing Science and Technology Commission(Grant No.cstc2020jcyj-msxmX0723)the Research Foundation of Chongqing Educational Committee(Grant No.KJQN2021000529)supported by the National Natural Science Foundation of China(Grant Nos.11871127,11971463)。
文摘Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive integer.We give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphismφ:A→Mn(B).We give an equivalent characterization of McDuff Ⅱ_(1) factors.We show that,if A is a unital nuclear C^(∗)-algebra and B is a type Ⅱ_(1) factor with faithful traceτ,then every unital^(∗)-homomorphism φ:A→M_(n)(B)is weakly approximately diagonalizable.If B is a unital simple infinite dimensional separable nuclear C^(∗)-algebra,then any finitely many elements in Mn(B)can be simultaneously weakly approximately diagonalized while the elements in the diagonals can be required to be the same.
基金supported by National Natural Science Foundation of China(Grant No.11371222)Natural Science Foundation of Shandong Province(Grant No.ZR2012AM024)
文摘Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.
