• East Asian mathematical journal
• /
• v.16 no.1
• /
• pp.49-55
• /
• 2000

In this paper we find some classes of operators implying normaity. The main result is as follows. If T is restriction-convexoid and is reduced by each of its eigenspaces corresponding to isolated eigenvalues, which is a class including hyponormal operators, and if $\sigma$(T) is countable then T is diagonal and normal.