Geodesic
Structural Properties of Elementary Operators
Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1485-1524

Voir la notice de l'article provenant de la source Cambridge University Press

Let and denote complex Banach algebras and let b e a left Banach module and a right Banach -module. If we define the bounded linear elementary operator R(A, B), acting on , by For the case , elementary operators were introduced by Lumer and Rosenblum [19], who studied their spectral properties. In this setting many authors subsequently studied spectral, algebraic, metric, and structural properties of elementary operators, with particular attention devoted to the inner derivations δa (δa(x) = ax – xa) [25], generalized derivations τ(a, b) (τ(a, b)(x) = ax – xb) [9, 10], and elementary multiplications S(a, b) (S(a, b)(x) = axb), including left and right multiplications La and Rb [11]. 
Apostol, Constantin; Fialkow, Lawrence. Structural Properties of Elementary Operators. Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1485-1524. doi: 10.4153/CJM-1986-072-6
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