Abstract:

LetHbe a complex Hilbert space with dimH>2, B(H) denote the algebra of all linear bounded operators on [WTHT]H. [WTBZ]We say that a linear mappi

ng  from B(H) into B(H) is an orthogonal derivable linear mapping if (A)*B+A*(B)=(A)B*+A(B)*=0 for any A,B∈B(H) with A*B=AB*=0.  Every orthogonal derivable linear mapping on B(H) is a generalized inner derivation.

Key words: orthogonality; orthogonal derivable mapping; projecti on; derivation