Let P denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any ...Let P denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any congruence either contains P or its join with P is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.展开更多
We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Pro...We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.展开更多
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
Let H olenote a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator T ∈ L(H) is said to be strongly irreducible if T does not commute with any nontrivial idemp...Let H olenote a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator T ∈ L(H) is said to be strongly irreducible if T does not commute with any nontrivial idempotent. Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum. This result can be considered as an "approximate inverse" of the Riesz decomposition theorem. In the paper, we give a more precise characterization of approximate invariants of strongly irreducible operators. The main result is: For any T ∈ L(H) with connected spectrum and ε > 0, there exists a strongly irreducible operator A, such that A - T < ε, V (A (A)) =～ N, K0(A (A)) ～= Z, and A (A)/rad A (A) is commutative, where A (A) denotes the commutant of A and rad A (A) denotes the Jacobson radical of A (A). The research is inspired by the recent similarity classification technique of Cowen-Douglas operators of Jiang Chunlan.展开更多
基金The NSF(ZR2010AL004)of Shandong Province of China
文摘Let P denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any congruence either contains P or its join with P is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.
基金The 973 Project of China and the NNSF (Grant No. 19631070) of China.
文摘We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.
文摘In this paper, we introduce O-F-inverse semigroups and characterize O-F-inverse categorical semigroups by using their minimal primitive congruence β.
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supported by the National Natural Science Foundation of China (Grant No. 10571041)Hebei Provincial Natural Science Foundation (Grant No. A2005000006)
文摘Let H olenote a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator T ∈ L(H) is said to be strongly irreducible if T does not commute with any nontrivial idempotent. Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum. This result can be considered as an "approximate inverse" of the Riesz decomposition theorem. In the paper, we give a more precise characterization of approximate invariants of strongly irreducible operators. The main result is: For any T ∈ L(H) with connected spectrum and ε > 0, there exists a strongly irreducible operator A, such that A - T < ε, V (A (A)) =～ N, K0(A (A)) ～= Z, and A (A)/rad A (A) is commutative, where A (A) denotes the commutant of A and rad A (A) denotes the Jacobson radical of A (A). The research is inspired by the recent similarity classification technique of Cowen-Douglas operators of Jiang Chunlan.
