On the set of orthogonally additive functions with orthogonally additive second iterate

Orthogonally Additive Polynomials on Spaces of Continuous Functions

We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y , there exists a linear operator S : C(K) −→ Y such that P (f) = S(f). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.

Orthogonally Additive Polynomials on C*-algebras

Let A be a C*-algebra which has no quotient isomorphic to M2(C). We show that for every orthogonally additive scalar nhomogeneous polynomials P on A such that P is Strong* continuous on the closed unit ball of A, there exists φ in A∗ satisfying that P (x) = φ(x), for each element x in A. The vector valued analogue follows as a corollary.

Σ-null-additive Set Functions

There is introduced the notion of σ-null-additive set function as a generalization of the classical measure. There are proved the relations to disjoint and chain variations. The general Lebesgue decomposition theorem is obtained. AMS Mathematics Subject Classification (2000): 28A25

Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

On the Stability of the Orthogonally Quartic Functional Equation