All-derivable points of operator algebras Original Research Article

Let image be an operator subalgebra in B(H), where H is a Hilbert space. We say that an element image is an all-derivable point of image for the norm-topology (strongly operator topology, etc.) if, every norm-topology (strongly operator topology, etc.) continuous derivable linear mapping φ at Z (i.e. φ(ST)=φ(S)T+Sφ(T) for any image with ST=Z) is a derivation. In this paper, we show that every invertible operator in the nest algebra image is an all-derivable point of the nest algebra for the strongly operator topology. We also prove that every nonzero element of the algebra of all 2×2 upper triangular matrixes is an all-derivable point of the algebra.