Isomorphisms and Derivations in LieC*-Algebras

Choonkil Park,Jianlian Cui,Jong Su An

doi:10.1155/2007/85737

Choonkil Park, Jianlian Cui + Show 1 more

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https://doi.org/10.1155/2007/85737

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Abstract

We investigate isomorphisms betweenC*-algebras, LieC*-algebras, andJC*-algebras, and derivations onC*-algebras, LieC*-algebras, andJC*-algebras associated with the Cauchy–Jensen functional equation2f((x+y/2)+z)=f(x)+f(y)+2f(z).

Highlights

Introduction and preliminariesUlam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems, containing the stability problem of homomorphisms
Rassias [3] provided a generalization of Hyers’ theorem which allows the Cauchy difference to be unbounded: Let f : E → E be a mapping from a normed vector space E into a Banach space E subject to the inequality f (x + y) − f (x) − f (y) ≤ x p + y p for all x, y ∈ E, where and p are constants with > 0 and p < 1
This new concept is known as HyersUlam-Rassias stability of functional equations

Summary

Introduction

Introduction and preliminariesUlam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems, containing the stability problem of homomorphisms. Rassias [3] provided a generalization of Hyers’ theorem which allows the Cauchy difference to be unbounded: Let f : E → E be a mapping from a normed vector space E into a Banach space E subject to the inequality f (x + y) − f (x) − f (y) ≤ x p + y p for all x, y ∈ E, where and p are constants with > 0 and p < 1. Rassias [15] provided an alternative generalization of Hyers’ stability theorem which allows the Cauchy difference to be unbounded, as follows.

Results

Conclusion