Hypergraph partitions
We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.
cs.DS↗
arXiv subjects
Chao You
Publications and source records attributed to Chao You.
Vector bundles from generalized pairs of cocycles
It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still determine vector bundles.
math.KT↗
On C*-algebras related to constrained representations of a free group
We consider representations of the free group $F_2$ on two generators such that the norm of the sum of the generators and their inverses is bounded by $μ\in[0,4]$. These $μ$-constrained representations determine a C*-algebra $A_μ$ for each $μ\in[0,4]$. We prove that these C*-algebras form a continuous bundle of C*-algebras over $[0,4]$ and calculate their K-groups.
math.OA↗
Simplified and Equivalent Characterizations of Banach Limit Functional and Strong Almost Convergence
In this paper, we give simplified and equivalent characterizations of Banach limit functional, which is the minimum requirement to characterize strong almost convergence. With this machinery, we show that Hajdukovic's quasi-almost convergence is equivalent to strong almost convergence.
math.FA↗
General solutions to equation $axb^*-bx^*a^*=c$ in rings with involution
In [Q. Xu et al., The solutions to some operator equations, Linear Algebra Appl.(2008), doi:10.1016/j.laa.2008.05.034], Xu et al. provided the necessary and sufficient conditions for the existence of a solution to the equation $AXB^*-BX^*A^*=C$ in the general setting of the adjointable operators between Hilbert $C^*$-modules. Based on the generalized inverses, they also obtained the general expression of the solution in the solvable case. In this paper, we generalize their work in the more general setting of ring $R$ with involution * and reobtain results for rectangular matrices and operators between Hilbert $C^*$-modules by embedding the "rectangles" into rings of square matrices or rings of operators acting on the same space.
math.RA↗
On distribution and almost convergence of bounded sequences
In this paper, we give the concepts of properly distributed and simply distributed sequences, and prove that they are almost convergent. Basing on these, we review the work of Feng and Li [Feng, B. Q. and Li, J. L., Some estimations of Banach limits, J. Math. Anal. Appl. 323(2006) No. 1, 481-496. MR2262220 46B45 (46A45).], which is shown to be a special case of our generalized theory.
math.FA↗
On Almost Representations of Property (T) Groups
Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of A.Zuk, a similar dichotomy holds for almost representations as well.
math.OA↗