In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassiasstability of n-jordan *-homomorphisms on C*-algebras.

By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation from the unit interval into the reals, or by signed measures on the Borel-subsets. Each of these objects has an (even minimal) Jordan decomposition into non-n...

We prove that the trace of the nth power of the antipode of a Hopf algebra with the Chevalley property is a gauge invariant, for each integer n. As a consequence, the order of the antipode, and its square, are invariant under Drinfeld twists. The invariance of the order of the antipode is closely related to a question of Shimizu on the pivotal covers of finite tensor categories, which we affirm...

We refine the notion of variety over the “field with one element” developed by C. Soulé by introducing a grading in the associated functor to the category of sets, and show that this notion becomes compatible with the geometric viewpoint developed by J. Tits. We then solve an open question of C. Soulé by proving, using results of J. Tits and C. Chevalley, that Chevalley group schemes are exampl...

Participants pressed computer keys to keep a moving dot stimulus within a rectangle, either alone or with a partner they could neither see nor hear. Pressing the A-key or L-key caused the dot to move right or left, respectively, for as long as the key was pressed. Switching between the A and L keys (i.e., turning) proved challenging: concurrently pressing both keys made the stimulus move upward...

(1) mT (x) = p1 (x) s1 · · · pk (x)k These irreducible factors can then be used to construct certain polynomials f1 (x) , . . . , fk (x) and corresponding operators Ei ≡ fi (T ) which can be used to decompose the vector space V into a direct sum of T -invariant subspaces V = V1 ⊕ V2 ⊕ · · · ⊕ Vk Morever, we have both Vi = Ei (V ) (the image of V under Ei) and Vi = ker (pi (T ) i) (the kernel of...

In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that Z[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, ...

In this paper, we essentially classify those finite 3-groups G having integral group rings with the multiplicative Jordan decomposition property. If G is abelian, then it is clear that Z[G] satisfies MJD. Thus, we are only concerned with the nonabelian case. Here we show that Z[G] has the MJD property for the two nonabelian groups of order 33. Furthermore, we show that there are at most three o...

The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean Jordan algebras says that when the sum of a Fréchet differentiable function Θ(x) and a spectral function F (x) is minimized over a spectral set Ω, any local minimizer a operator commutes with the Fréchet derivative Θ′(a). In this paper, we extend this result to sets and functions which are (just) inv...