Abstract. In this paper, we study spectral properties of class $wF(p,r,q)$ operators for $p+r\leq1$ and $q\geq1$. We show that if $T$ belongs to class $wF(p,r,q)$ operators, then the nonzero points of its point spectrum and joint point spectrum are identical, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical, and Putnam's theorems hold for class $wF(p,r,q)$ operators.

AMS Subject Classification (1991): 47B20, 47A30

Keyword(s): wF(p, class, r, q), (joint) point spectrum, (joint) approximate point spectrum, Berberian's theorem, Putnam's theorems

Received July 28, and in revised form December 30, 2004. (Registered under 5899/2009.)