arXiv subjects
Publications and source records attributed to Bin Meng.
In this paper, we investigate operator-valued frames with the structure of group-like unitary system. We show the commutant of the group-like unitary system can be characterized in terms of analysis operators associated with all the operator-valued Bessel generators and give some sufficient and necessary conditions to describe when an operator-valued frame generator admits a Parseval dual.
Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some results concerning dilation, alternate dual, and existence of operator-valued frames are given. Then we characterize the optimal operator-valued frames under the case which one packet of data is lost in transmission. At last we construct the operator-valued frames $\{V_j\}_{j=1}^m$ with given frame operator $S$ and satisfying $V_jV_j^*=α_jI$, where $α_j's$ are positive numbers.
The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates. We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R.Morgan in [R.Morgan, A restarted GMRES method augmented with eigenvectors, SIAM J.Matrix Anal.Appl. 16 (1995)1154-1171]. We derive the implementation of this method and present some numerical examples to show the advantages of this method.
In this paper, we characterize a class of additive maps on Hilbert $C^\ast$-modules which maps a "rank one" adjointable operators to another rank one operators.
In this paper, we characterize rank one preserving module maps on a Hilbert $C^\ast-$module and study its applications on free probability theory.
We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for $Φ^\ast_{M_2(\mb)}(A,A^\ast,M_2(\mb),η)$, where $A\in M_2(\mb)$ is a $2\times 2$ operator matrix on $\mb$, and $η$ is linear operators on $M_2(\mb)$. Then we consider a special setting: $A$ is an operator-valued semicircular matrix with conditional expectation covariance, and find that $Φ_\mb^\ast(c,c^\ast:\mb,id)=2Index(E)$, where $E$ is a conditional expectation of $\mb$ onto $\md$ and $c$ is a circular variable with covariance $E$.