Properties of p-hyponormal composition operators on L²(m)

Abstract

In this thesis, we characterize p-hyponormal composition operators with 0<p≤1 on L²(m). In particular, we get the following equivalent statements. (a)C_(T) is p-hyponormal where 0<p≤1, (b)M_(f)^(P)_(T)>M_(f)^(P)_(T)。_(T)P , where P is an orthogonal projection of L²(m) onto the closure of range of C_(T), and (c)∥f^(P/2)_(T)g∥≥∥(f_(T)。T)^(p/2)Pg∥ for all ∈L²(m). Also we show that if C_(T) is p-hyponormal, the Radon-Nikodym derivative f_(T) is positive.;이 논문에서는 composition 작용소가 p-hyponormal이 되기위한 필요충분조건들에 대해 공부한다. 또한, composition 작용소가 p-hyponormal 일때 Radon-Nikodym derivative 함수가 positive가 됨을 증명한다.