Representable states on quasilocal quasi *-algebras

Abstract

Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a compatible family of local states to give rise to a global state. Some properties of local modifications of representable states and some aspects of their asymptotic behavior are also considered.

On Central Complete and Incomplete Bell Polynomials I

“…Here, we recall that the central factorial numbers T(n, k) of the second kind and the central Bell polynomials B n (x). The incomplete and complete Bell polynomials have applications in such diverse areas as combinatorics, probability, algebra, modules over a * -algebra (see [1,2]), quasi local algebra and analysis. Here, we recall some applications of them and related works.…”

“…A systematic treatment of these important numbers was given in [11], including their properties and applications to difference calculus, spline theory, and to approximation theory, etc. For some other related references on central factorial numbers, we let the reader refer to [1,2,[12][13][14]. Here, we note that central Bell polynomials and central factorial numbers of the second kind are respectively 'central' analogues for Bell polynomials and Stirling numbers of the second kind.…”

On the Decomposability of the Linear Combinations of Euler Polynomials with Odd Degrees

“…These polynomials play a central role in various branches of mathematics; for example, in various approximation and expansion formulas in discrete mathematics and in number theory (see for instance [1,2]), in p-adic analyis (see [3], Chapter 2), in statistical physics as well as in semi-classical approximations to quantum probability distributions (see [4][5][6][7]).…”

Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras

“…Representability of a positive linear functional on a quasi *-algebra is a topical problem, see e.g. [6,2], and it is of a certain interest in some application see, for instance, [3] and references therein. In this paper, starting from a hermitian linear functional ω defined on a quasi *-algebra (A, A 0 ) without unit, we study under what conditions it is possible to extend ω to a representable linear functional, defined on a quasi *-algebra with unit, possibly the whole unitization of (A, A 0 ).…”

“…the functional ω is extensible to the unitized quasi *-algebra.Proof. Let us consider the functional ω e defined in(3). Property (HB) holds for ω 0 = ω ↾ A 0 by Lemma 3.4.…”