Higher *-derivations between unital C*-algebras
Journal Title: Surveys in Mathematics and its Applications - Year 2010, Vol 5, Issue 0
Abstract
Let A, B be two unital C<SUP>*</SUP>-algebras. We prove that every sequence of mappings from A into B, H = {h<SUB>0</SUB>,h<SUB>1</SUB>, ..., h<SUB>m</SUB>, ...}, which satisfy h<SUB>m</SUB>(3<SUP>n</SUP>uy) =Σ<SUB>i+j=m</SUB>h<SUB>i</SUB>(3<SUP>n</SUP>u)h<SUB>j</SUB>(y) for each m ∈ <B>N</B><SUB>0</SUB>, for all u∈U(A), all y∈ A, and all n = 0, 1, 2, ..., is a higher derivation. Also, for a unital C<SUP>*</SUP>-algebra A of real rank zero, every sequence of continuous mappings from A into B, H = {h<SUB>0</SUB>,h<SUB>1</SUB>,..., h<SUB>m</SUB>, ...}, is a higher derivation when h<SUB>m</SUB>(3<SUP>n</SUP>uy)=Σ<SUB>i+j=m</SUB>h<SUB>i</SUB>(3<SUP>n</SUP>u)h<SUB>j</SUB>(y) holds for all u∈I<SUB>1</SUB>(A<SUB>sa</SUB>), all y∈ A, all n = 0, 1,2, ... and for each m ∈ <B>N</B><SUB>0</SUB>. Furthermore, by using the fixed points methods, we investigate the Hyers-Ulam-Rassias stability of higher *-derivations between unital C<SUP>*</SUP>-algebras.
Authors and Affiliations
M. Eshaghi Gordji, R. Farokhzad Rostami, S. Hosseinioun
Keywords
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