All-derivable points in nest algebras

✍ Scribed by Lin Zhang; Jun Zhu; Junde Wu

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 169 KB
• Volume: 433
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.01.034

✦ Synopsis

Suppose that A is an operator algebra on a Hilbert space H. An element V in A is called an all-derivable point of A for the strong operator topology if every strong operator topology continuous derivable mapping ϕ at V is a derivation. Let N be a complete nest on a complex and separable Hilbert space H. Suppose that M belongs to N with {0} / = M / = H and write M for M or M ⊥ . Our main result is: for any Ω ∈ alg N with Ω = P( M)ΩP( M), if Ω| M is invertible in alg N M , then Ω is an all-derivable point in alg N for the strong operator topology.