SOME ACHIEVEMENTS ON TWO VARIABLES $\sigma$-derivations

Authors

  • Amin Hosseini

DOI:

https://doi.org/10.30495/jme.v8i0.261

Keywords:

-derivation, two variables -derivation, two variables derivation,

Abstract

Let

B and A be two Banach algebras and M be a Banach B

 

: A ! B

 

-

: A × A ! M is called a two variables -derivation whenever -(ab, c

 

-

(a, c)(b)+(a)-(b, c) and -(a, bc) = -(a, b)(c)+(b)-(a, c) for all a, b, c 2 A

 

A and B are unital and - : A × A ! B

 

-derivation such that -(1, a0) = 1 for some a0 2 A then

 

is symmetric, i.e.

-(a, b) = -(b, a

 

: A ! B such that -(a, b) = (ab)(a0)−1

 

.

) and there exists a unital homomorphism

-

is a

two variables

 

.

In this paper, we prove that if

 

) =

is a linear mapping. A bilinear map

bimodule.

Suppose that

 

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Published

2015-01-05

Issue

Section

Vol. 8, No. 4, (2014)