11 papers
Strongly irreducible operators, -groups, and Jones indices in the hyperfinite type factor
Junsheng Fang, Chunlan Jiang, Minghui Ma +1
In this paper, we study the strong irreducibility of a class of operators associated with irrational rotation algebras in the hyperfinite type factor .…
Equivalence of states and bimodule quantum channels
Linzhe Huang, Chunlan Jiang, Zhengwei Liu +1
We study the action of quantum channels on states on a von Neumann algebra with conserved quantities encoded by a subalgebra . We define a phase as an eq…
Kaplansky's second test problem in operator algebras
Chunlan Jiang, Minghui Ma, Rui Shi +1
Kaplansky's second test problem on similarity asks: if and are elements in a unital Banach algebra and is similar to in $\mathbb{M}_2(…
Intertwining Properties for Bimodule Quantum Markov Semigroups
Chunlan Jiang, Jincheng Wang, Jinsong Wu
In this paper, we study the Bakry-Émery estimates for GNS- and KMS-symmetric semigroups in terms of the Fourier multiplier of the gradient form and the iterated gradient form in th…
Completely Bounded Representations Into Von Neumann Algebras And Connes Embedding Problem
Junsheng Fang, Chunlan Jiang, Liguang Wang +1
In this paper, we prove that if is a unital separable -algebra, is a von Neumann algebra which has the Kirchberg's quotient weak expectation proper…
Bimodule KMS Symmetric Quantum Markov Semigroups and Gradient Flows
Chunlan Jiang, Jincheng Wan, Jinsong Wu
The bimodule KMS symmetry of a bimodule quantum Markov semigroup extends the classical KMS symmetry of a quantum Markov semigroup. Compared with (bimodule) GNS symmetry, the (bimod…
On Klee's problem of convex bodies in Banach spaces
Lixin Cheng, Chunlan Jiang, Liping Yuan
It is well known that every convex body in a finite dimensional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infi…
A local quantization principle for inclusions of tracial von Neumann algebras
Xinyan Cao, Junsheng Fang, Chunlan Jiang +1
We study the local quantization principle (after Sorin Popa~\cite{popa 94} and \cite{popa 95}) of inclusions of tracial von Neumann algebras. Let be a type ${\rm…
The invariant subspace problem and Rosenblum operators I
Junsheng Fang, Bingzhe Hou, Chunlan Jiang +1
Let be an invertible operator. From the 1940's, Gelfand, Hille and Wermer investigated the invariant subspaces of by analyzing the growth of , wh…
Density of irreducible operators in the trace-class norm
Junsheng Fang, Chunlan Jiang, Minghui Ma +3
In 1968, Paul Halmos initiated the research on density of the set of irreducible operators on a separable Hilbert space. Through the research, a long-standing unsolved problem inqu…
Phase Group Categories of Bimodule Quantum Channels
Linzhe Huang, Chunlan Jiang, Zhengwei Liu +1
In this paper, we study the quantum channel on a von Neuamnn algebra preserving a von Neumann subalgebra , namely an --bimodule…