All-derivable points of operator algebras

✍ Scribed by Jun Zhu

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 112 KB
• Volume: 427
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.05.049

✦ Synopsis

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 + Sϕ(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.