Abstract

In this paper, we investigate homomorphisms in proper CQ-algebras, proper Lie CQ-algebras and proper Jordan CQ-algebras and deriva-tions on proper CQ-algebras, proper Lie CQ-algebras and proper JordanCQ-algebras associated with the Cauchy-Jensen functional equation2f(x + y2+ z)= f(x) + f(y) + 2f(z);which was introduced and investigated in [3, 28].Furthermore, Isometries and isometric isomorphisms in proper CQ-algebrasare studied.

Highlights

  • Introduction and preliminariesTopological quasi ∗-algebras have been considered with a certain interest, first for their own mathematical structure and second for their possible applications in the mathematical description of a number of quantum models

  • We will prove the superstability of isomorphisms and derivations in proper CQ∗-algebras, of homomorphisms and derivations in proper Lie CQ∗algebras and of homomorphisms and derivations in proper Jordan CQ∗-algebras associated with the Cauchy-Jensen additive functional inequality

  • We will prove the superstability of isometries and isometric isomorphisms in proper CQ∗-algebras associated with the Cauchy-Jensen additive functional inequality (1.2)

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Summary

Introduction

Introduction and preliminariesTopological quasi ∗-algebras have been considered with a certain interest, first for their own mathematical structure and second for their possible applications in the mathematical description of a number of quantum models. We use a different algebraic structure, similar to the one considered in [12], which is suggested by the considerations above: because of the relevance of the unbounded operators in the description of S, we will assume that the observables of the system belong to a quasi ∗-algebra (A, A0) (see [44] and references therein), while, in order to have a richer mathematical structure, we will use a slightly different algebraic structure: (A, A0) will be assumed to be a proper CQ∗-algebra, which has nicer topological properties. Lee et al [21] proved the Hyers-Ulam stability of an additive functional inequality in proper CQ∗-algebras.

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