10 citations · 20 across the 15 of their papers we have counts for
15 papers
The similarity of irreducible operators in factors
Minghui Ma, Rui Shi, Shanshan Yang
An operator in a separable factor is said to be irreducible in if the von Neumann subalgebra generated by is an irreducible subfactor o…
Normed ideal perturbation of irreducible operators in semifinite von Neumann factors
Rui Shi
In [10], Halmos proved an interesting result that the set of irreducible operators is dense in in the sense of Hilbert-Schmidt approximation. In a von Neum…
Reducible operators in non- type factors
Junhao Shen, Rui Shi
A famous question of Halmos asks whether every operator on a separable infinite-dimensional Hilbert space is a norm limit of reducible operators. In [30], Voiculescu gave this prob…
On irreducible operators in factor von Neumann algebras
Junsheng Fang, Rui Shi, Shilin Wen
Let be a factor von Neumann algebra with separable predual and let . We call an irreducible operator (relative to ) if is an…
Approximate equivalence of representations of AH algebras into semifinite von Neumann factors
Junhao Shen, Rui Shi
In this paper, we prove a non-commutative version of the Weyl-von Neumann theorem for representations of unital, separable AH algebras into countably decomposable, semifinite, prop…
A note on the Voiculescu's theorem for commutative C-algebras in semifinite von Neumann algebras
Don Hadwin, Rui Shi
In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital -homomorphisms…
Perturbations of self-adjoint operators in semifinite von Neumann algebras: Kato-Rosenblum theorem
Qihui Li, Junhao Shen, Rui Shi +1
In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let be a countably decomposable, properly infinite, semifinite v…
A generalization of the Voiculescu theorem for normal operators in semifinite von Neumann algebras
Qihui Li, Junhao Shen, Rui Shi
In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful norm…
On a class of operators in the hyperfinite factor
Zhangsheng Zhu, Junsheng Fang, Rui Shi
Let be the hyperfinite factor and let be two generators of such that and for an irrational number . In this paper we st…
Unitary operators in the orthogonal complement of a type von Neumann algebra in a type factor
Xiaoyan Zhou, Rui Shi
It is well-known that the equality holds for an i.c.c. group and a subgroup in , where…
A reduction theory for operators in type von Neumann algebras
Rui Shi
In this paper, we study the structure of operators in a type von Neumann algebra . Inspired by the Jordan canonical form theorem, our main motivation…
A similarity invariant of a class of n-normal operators in terms of K-theory
Chunlan Jiang, Rui Shi
In this paper, we prove an analogue of the Jordan canonical form theorem for a class of -normal operators on complex separable Hilbert spaces in terms of von Neumann's reduction…
Direct integrals of strongly irreducible operators
Chunlan Jiang, Rui Shi
Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written a…
On The Uniqueness of The Strongly Irreducible Decompositions of Operators up to Similarity
Rui Shi
We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of direct integrals. Precisely, w…
On a generalization of the Jordan canonical form theorem on separable Hilbert spaces
Rui Shi
We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.