In this paper, the authors give a new proof of Block and Weinberger’s Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra.
We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self abs...We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self absorbing C^(*)-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_(2)),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(resp.properly infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.展开更多
Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).The...Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2(m+1)-almost divisible(weakly m-almost divisible,secondly weakly(m,n)-divisible).展开更多
We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms,and characterize them in terms of the corres...We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms,and characterize them in terms of the corresponding transformation groupoids and their operator algebras.In particular,we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving C^(∗)-isomorphism between the associated transformation groupoid C^(∗)-algebras.We also give some examples of orbit equivalence,consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.展开更多
In this note, we give complete descriptions of the structure of the monotone product of two yon Neumann algebras and two C^＊-algebras. We show that the monotone product of two simple yon Neumann algebras and C^＊-alg...In this note, we give complete descriptions of the structure of the monotone product of two yon Neumann algebras and two C^＊-algebras. We show that the monotone product of two simple yon Neumann algebras and C^＊-algebras aren＇t simple again. We also show that the monotone product of two hyperfinite yon Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.展开更多
In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra...In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite C^*-algebras.展开更多
We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an ap...We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.展开更多
Given two nuclear C^＊-algebras A1 and A2 with states φ1 and φ2, we show that the monotone product C^＊-algebra A1 △→ A2 is still nuclear. Furthermore, if both the states φ1 and φ2 are faithful, then the monoton...Given two nuclear C^＊-algebras A1 and A2 with states φ1 and φ2, we show that the monotone product C^＊-algebra A1 △→ A2 is still nuclear. Furthermore, if both the states φ1 and φ2 are faithful, then the monotone product ,A1 △→ A2 is nuclear if and only if the C^＊-algebras ,A1 and A2 both are nuclear.展开更多
We give an overview of the question： which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the ques...We give an overview of the question： which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive elements can be written as a sum of finitely many projections. We focus on von Neumann Mgebras, on purely infinite simple C^＊-algebras, and on their associated multiplier algebras.展开更多
Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an a...Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved.展开更多
基金Supported by NSFC(Nos.11401256,11501249,11871342)Zhejiang Provincial Natural Science Foundation of China(No.LQ13A010016)the Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202249575)。
基金This work was supported by the National Natural Science Foundation of China(Nos.11811530291,11831006,11771092)。
文摘In this paper, the authors give a new proof of Block and Weinberger’s Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra.
基金supported by the Research Center for Operator Algebras at East China Normal University which is funded by the Science and Technology Commission of Shanghai Municipality (Grant No.13dz2260400)National Natural Science Foundation of China (Grant No.11531003)+1 种基金Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice (Grant No.1361431)the special fund for the Short-Term Training of Graduate Students from East China Normal University。
文摘We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self absorbing C^(*)-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_(2)),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(resp.properly infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.
基金supported by National Natural Sciences Foundation of China(11501357,11571008)supported by National Natural Sciences Foundation of China(11871375)。
文摘Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2(m+1)-almost divisible(weakly m-almost divisible,secondly weakly(m,n)-divisible).
基金Supported by the NSF of China(Grant No.12271469,11771379,11971419)。
文摘We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms,and characterize them in terms of the corresponding transformation groupoids and their operator algebras.In particular,we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving C^(∗)-isomorphism between the associated transformation groupoid C^(∗)-algebras.We also give some examples of orbit equivalence,consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.
基金the Youth Foundation of Sichuan Education Department(China)(2003B017)the National Natural Science Foundation of China(10301004)
文摘In this note, we give complete descriptions of the structure of the monotone product of two yon Neumann algebras and two C^＊-algebras. We show that the monotone product of two simple yon Neumann algebras and C^＊-algebras aren＇t simple again. We also show that the monotone product of two hyperfinite yon Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.
文摘In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite C^*-algebras.
基金Supported by National Natural Sciences Foundation of China(Grant Nos.11501357 and 11571008)。
文摘We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.
基金the Youth Foundation of Sichuan Education Department (No.2003B017)the Doctoral Foundation of Chongqing Normal University (No.08XLB013)
文摘Given two nuclear C^＊-algebras A1 and A2 with states φ1 and φ2, we show that the monotone product C^＊-algebra A1 △→ A2 is still nuclear. Furthermore, if both the states φ1 and φ2 are faithful, then the monotone product ,A1 △→ A2 is nuclear if and only if the C^＊-algebras ,A1 and A2 both are nuclear.
文摘We give an overview of the question： which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive elements can be written as a sum of finitely many projections. We focus on von Neumann Mgebras, on purely infinite simple C^＊-algebras, and on their associated multiplier algebras.
基金supported by the National Natural Science Foundation of China(No.11371279)the Shandong Provincial Natural Science Foundation of China(No.ZR2015PA010)
文摘Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved.
