JORDAN *-HOMOMORPHISMS BETWEEN UNITAL C^*-ALGEBRAS

Hyers-Ulam Stability of Mappings From a Ring a Into an a-Bimodule

“…If p ≥ 1 however, the sequence (3 −n θ3 np ) n does not converge and this equality may fail to hold. For this reason, Theorem 2.3, of [6] need not hold.…”

“…In the same paper [6], Eshaghi Gordji et al give the following assertion: Theorem 2.3 ([6, Theorem 2.4]). Let A and B be unital C * -algebras and f : A → B a mapping for which there exists a function ϕ : A 3 → R + such that:…”

“…In this paper, after the foregoing introductory section, we will first give in Section 2 several comments on the paper [6]. We will show that some assertions therein are inexact.…”

“…In Section 3, we deal with additive mappings from a linear space A into a Banach space B and establish (see Theorem 3.1) their Hyers-Ulam-Gȃvruta-stability with respect to the following equation introduced in [6]:…”

“…In the real case this is only {−1, 1}. [6] In [6], Eshaghi Gordji et al give the following result asserting the supper stability of Jordan * -homomorphisms between C * -algebras:…”