Weakly Approximate Diagonalization of Homomorphisms into Finite von Neumann Algebras  

作　　者：Wen Hua QIAN Jun Hao SHEN Wen Ming WU 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China [2]Department of Mathematics and Statistics,University of New Hampshire,Durham,NH 03824,USA

出　　处：《Acta Mathematica Sinica,English Series》2024年第9期2187-2194,共8页数学学报（英文版）

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)。

摘　　要：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.

关 键 词：Weakly approximately diagonalizable McDuff factors NUCLEAR hyperfinite 

分 类 号：O15[理学—数学]