Let ,4 be an unital Banach algebra with the unital element I. We denote the set of （n × n）-matrices over ,4 by Mn（.A）. The set of idempotent elements of ,4 is denoted by
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's suf...This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.展开更多
A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0(R)+, i.e., [eR]∧[fR] = 0. In this pa...A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0(R)+, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].展开更多
Let Ω be a finite set, and let G be a permutation group on Ω. A subset H of G is called intersecting if for any a, 7r H, they agree on at least one point. We show that a maximal intersecting subset of an irreducible...Let Ω be a finite set, and let G be a permutation group on Ω. A subset H of G is called intersecting if for any a, 7r H, they agree on at least one point. We show that a maximal intersecting subset of an irreducible imprimitive reflection group G（m,p,n） is a coset of the stabilizer of a point in {1,... ,n} provided n is sufficiently large.展开更多
基金The NSFC (10471025) the NSF of Fujian Province of China (F0210014 and Z0511019).
文摘Let ,4 be an unital Banach algebra with the unital element I. We denote the set of （n × n）-matrices over ,4 by Mn（.A）. The set of idempotent elements of ,4 is denoted by
基金supported by the National Natural Science Foundation of China(Grant No.10471025)the Natural Science Foundation of Fujian Province of China(Grant Nos.F0210014&Z0511019).
文摘This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.
基金the National Natural Science Foundation of China （No. 10571080） the Natural Science Foundation of Jiangxi Province （No. 0611042） the Science and Technology Projiet Foundation of Jiangxi Province （No. G[20061194） and the Doctor Foundation of Jiangxi University of Science and Technology.
文摘A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0(R)+, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].
基金Acknowledgements The author would like to express her deep gratitude to Professor Jun Wang for guiding her into this area and thank the referees for their invaluable suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11001176, 10971138）.
文摘Let Ω be a finite set, and let G be a permutation group on Ω. A subset H of G is called intersecting if for any a, 7r H, they agree on at least one point. We show that a maximal intersecting subset of an irreducible imprimitive reflection group G（m,p,n） is a coset of the stabilizer of a point in {1,... ,n} provided n is sufficiently large.
