Related papers: On partial orders of operators
S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In this paper, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log…
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are…
In the present paper we introduce a lattice-ordered partial monoid structure on a suitable set of multilayer networks. We first study a kind of mappings that preserve the partial order and describe the order structure. After that we define…
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
In this article we present some new comparisons between the Heinz and Heron operator means, which improve some recent results known from the literature. We derive some refinements of these inequalities for unitarily invariant norms with the…
Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a…
Partial Markov categories are a recent framework for categorical probability theory that provide an abstract account of partial probabilistic computation with updating semantics. In this article, we discuss two order relations on the…
Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
This article contains a characterization of operator systems $\cS$ with the property that every positive map $\phi:\cS \rightarrow M_n$ is decomposable, as well as an alternate and a more direct proof of a characterization of decomposable…
This paper investigates the q-Stancu operators, which generalize the q-Bernstein operators, by developing a new representation in terms of the q-Pochhammer symbol. Based on this representation, some known properties are re-discovered, and a…