Abstract
Let A be an operator subalgebra in B ( H ) , where H is a Hilbert space. We say that an element Z ∈ A is an all-derivable point of A 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 + S φ ( T ) for any S , T ∈ A with ST = Z ) is a derivation. In this paper, we show that every invertible operator in the nest algebra alg N 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.
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