Related papers: Star operation on orders in simple Artinian rings

We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…

The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…

We consider normalized analytic function $f$ on the open unit disk for which either $\operatorname{Re} f(z)/g(z)>0$, $|f(z) /g(z) - 1|<1$ or $\operatorname{Re} (1-z^2) f(z) /z>0$ for some analytic function $g$ with $\operatorname{Re}…

Finding the optimal ordering of k-subsets with respect to an objective function is known to be an extremely challenging problem. In this paper we introduce a new objective for this task, rooted in the problem of star identification on…

Let $S$ be a subnormal operator on a separable complex Hilbert space $\mathcal H$ and let $\mu$ be the scalar-valued spectral measure for the minimal normal extension $N$ of $S.$ Let $R^\infty (\sigma(S),\mu)$ be the weak-star closure in…

We investigate the category of ``matricial order operator spaces,'' which generalize operator systems, being equipped with both matricial norms and matricial order. For these objects, we develop duality theory. Taking a cue from the theory…

The recursive path ordering is an established and crucial tool in term rewriting to prove termination. We revisit its presentation by means of some simple rules on trees (or corresponding terms) equipped with a 'star' as control symbol,…

After the introduction in 1994, by Okabe and Matsuda, of the notion of semistar operation, many authors have investigated different aspects of this general and powerful concept. A natural development of the recent work in this area leads to…

In this paper, we consider the problem of order preservation under addition and multiplication operators over the vector space of univariate real-valued random variables. Consistent with the case of usual order over the real numbers-as…

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…

Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…

We focus on Legendrian submanifolds of the space of one-jets of functions, $J^1(\mathbb{R}^n,\mathbb{R})$. We are interested in processes - operations - that build new Legendrian submanifolds from old ones. We introduce in particular two…

This article explains the relationship between analytic and algebraic order in case of abstract pseudo-differential operators for a regular spectral triple.

In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.

Let $f$ and $g$ be analytic functions on the open unit disk of the complex plane with $f/g$ belonging to the class $\mathcal{P} $ of functions with positive real part consisting of functions $p$ with $p(0)=1$ and $\operatorname{Re} p(z)>0$…

We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As…

The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C^*$-modules and their maps. Here we give a…

Let $R=\bigoplus_{\alpha\in\Gamma}R_{\alpha}$ be a graded integral domain. In this paper we study the space of homogeneous preserving semistar operations on $R$. We show if $\star$ is a homogeneous preserving semistar operation on $R$, then…

This paper provides some new characterizations of the diamond partial order for rectangular matrices by using properties of inner inverses, minus order, and SVD decompositions. In addition, the recently introduced 1MP generalized inverse…

We prove bounds for multilinear operators on $\R^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true…