arXiv subjects

Bui Ngoc Muoi

Publications and source records attributed to Bui Ngoc Muoi.

5 recordsLinked to original sources

arXiv2024

Characterizations of Strongly Entanglement Breaking channels for infinite-dimensional quantum systems

Entanglement breaking (EB) channels, as completely positive and trace-preserving linear operators, sever the entanglement between the input system and other systems. In the realm of infinite-dimensional systems, a related concept known as strongly entanglement breaking (SEB) channels emerges. This paper delves into characterizations of SEB channels, delineating necessary and sufficient conditions for a channel to be classified as SEB, especially with respect to the commutativity of its range. Moreover, we demonstrate that every closed self-adjoint subspace of trace-zero operators, with the trace norm, is the null space of a SEB channel.

math.FA↗

arXiv2022

Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets

Let $S$ be a right reversible semitopological semigroup, and let $\operatorname{LUC}(S)$ be the space of left uniformly continuous functions on $S$. Suppose that $\operatorname{LUC}(S)$ has a left invariant mean. Let $K$ be a weakly compact convex subset of a Banach space. We show that there always exists a common fixed point for any jointly weakly continuous and super asymptotically nonexpansive action of $S$ on $K$. Several variances involving the weak* compactness, the RNP, the distality of $K$ and/or the left reversibility of $S$ are also provided.

math.FA↗

arXiv2022

Optimal control problems governed by time-fractional diffusion equations with control constraint

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of optimal solutions for the optimal control problem. Then we derive first-and second-order optimality conditions for locally optimal solutions to the problem.

math.OC↗

arXiv2020

Bregman nonexpansive type actions of semitopological semigroups

Let $S$ be a semitopological semigroup, and let $C$ be a nonempty closed convex subset of a reflexive Banach space. Under some amenability conditions on $S$, we provide existence results of fixed points for several Bregman nonexpansive type actions $S\times C\to C$, $(s,x)\mapsto T_s x$, of $S$ on $C$. The mappings $T_s$ we discuss include those being Bregman generalized hybrid, Bregman nonspreading, and Bregman left asymptotically nonexpansive.

math.FA↗

arXiv2020

Super Asymptotically Nonexpansive Actions of Semitopological Semigroups on Frechet and Locally Convex Spaces

Let LUC$(S)$ be the space of left uniformly continuous functions on a semitopological semigroup $S$. Suppose that $S$ is right reversible and $\operatorname{LUC}(S)$ has a left invariant mean. Let $(X,d)$ be a Fréchet space. Let $τ$ be a locally convex topology of $X$ weaker than the $d$-topology such that the metric $d$ is $τ$-lower semicontinuous. Let $K$ be a $d$--separable and $τ$--compact convex subset of $X$. We show that every jointly $τ$-continuous and super asymptotically $d$-nonexpansive action $S\times K\mapsto K$ of $S$ has a common fixed point. Similar results in the locally convex space setting are provided.

math.FA↗