We prove that Jordan elementary surjective maps on rings are automatically additive. Elementary operators were originally introduced by Brešar and Šerml ([1]). In the last decade, elementary maps on operator algebras as well as on rings attracted more and more attentions. It is very interesting that elementary maps and Jordan elementary maps on some algebras and rings are automatically additive...

In two papers entitled “On a new foundation [Neue Begründung] of quantum mechanics,” Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formal...

In this paper, we examine some questions concerned with certain “skew” properties of the range of a Jordan *-derivation. In the first part we deal with the question, for example, when the range of a Jordan *-derivation is a complex subspace. The second part of this note treats a problem in relation to the range of a generalized Jordan *-derivation.

ion being made, in case the representation g is improper of the first kind, of the values of 0, at most denumerably infinite in number, where gi(8) is discontinuous. (19.9) rests on the fact (whose proof is trivial) that if fiim)(l) tends uniformly to the continuous f((t) when m—>, then if tm—H as m—>«>, we have lim/i(m)(í„) =/i(i) for m—>°o. The assertion is now easily proved that if (19.10...

Pseudo-Riemannian manifolds of balanced signature which are both spacelike and timelike Jordan Osserman nilpotent of order 2 and of order 3 have been constructed previously. In this short note, we shall construct pseudo-Riemannian manifolds of signature (2s, s) for any s ≥ 2 which are spacelike Jordan Osserman nilpotent of order 3 but which are not timelike Jordan Osserman. Our example and tech...

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...

Hyper/J supports a new approach to constructing, integrating and evolving software, called multi-dimensional separation of concerns. Developers can decompose and organize code and other artifacts according to multiple, arbitrary criteria (concerns) simultaneously—even after the software has been implemented—and synthesize or integrate the pieces into larger-scale components and systems. Hyper/J...

With the help of the Jordan–Wigner transformation the spin-12 XY chains can be reformulated in terms of noninteracting spinless fermions and, as a result, many statistical-mechanics calculations can be performed rigorously, i.e. without making any simplifying approximations. We are interested in dynamic properties of such chains (time-dependent spin correlation functions, dynamic structure fact...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

conclusions as the prevalence of hypomagnesaemia among patients with type 2 diabetes treated at the ncdeg was found to be 19% (95% ci, 16.8%-21.4%), we recommend periodic determination of magnesium level and appropriate magnesium replacement therapy particularly among the above defined groups. results out of 1105 patients with type 2 diabetes, 210 patients (19%) (95% ci, 16.8%-21.4%) were hypom...