The equation dd ′ + d ′ d = D 2 for derivations on C-algebras

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Let A be an algebra. A linear mapping d : A!A is called a derivation if d ( ab ) = d ( a ) b + ad ( b ) for each a;b 2A . Given two derivations d and d ′ on a C -algebra A , we prove that there exists a derivation D on A such that dd ′ + d ′ d = D 2 if and only if d and d ′ are linearly dependent.

PDF

___

[1] Barraa M, Pedersen S. On the product of two generalized derivations. Proc Amer Math Soc 1999; 127: 2679-2683.
[2] Creedon T. Products of derivations. Proc Edinburgh Math Soc 1998; 41: 407-410.
[3] Fong CK, Sourour AR. On the operator identity ∑ A k XB k 0. Canad J Math 1979; 31: 845-857.
[4] Kadison RV. Derivations of operator algebras. Ann Math 1966; 83: 280-293.
[5] Mathieu M. Properties of the product of two derivations of a C -algebra. Canad Math Bull 1989; 32: 490-497.
[6] Mathieu M. More properties of the product of two derivations of a C -algebra. Bull Austral Math Soc 1990; 42: 115-120.
[7] Mathieu M. Posners second theorem deduced from the rst. Proc Amer Math Soc 1992; 114: 601{602.
[8] Pedersen S. The product of two unbounded derivations. Canad Math Bull 1990; 33: 354-348.
[9] Posner EC. Derivations in prime rings. Proc Amer Math Soc 1957; 8: 1093-1100.
[10] Sakai S. Derivations of W -algebras. Ann Math 1966; 83: 273-279.