| dc.description.abstract | In the present paper, results on characterization of inner derivations in Banach algebras are discussed.Some techniques are employed for derivations due to Mecheri, Hacene, Bounkhel and Anderson. Let H be an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators on H. A generalized derivation δ: B(H) → B(H) is defined by δA,B(X) = AX −XB, for all X ∈ B(H) and A,B fixed in B(H). An inner derivation is defined by δA(X) = AX −XA, for all X ∈ B(H) and A fixed in B(H). Norms of inner derivations have been investigated by several mathematicians. However, it is noted that norms of inner derivations implemented by norm-attainable operators have not been considered to a great extent. In this study, we investigate properties of inner derivations which are strictly implemented by norm-attainable and we determine their norms. The derivations in this work are all implemented by norm-attainable operators. The results show that these derivations admit tensor norms of operators. | en_US |
