On Some Classes Of Operators Associated With Furuta Inequality And Aluthge Transformation

In this paper, we shall study classes of operators associated with Furuta inequality and Aluthge transformation, mainly class wF(p,r,q), class F(p,r,q) and so on. Next, we shall give several results on p-hyponormal and log-hyponormal operators.In ChapterⅠ, firstly, we introduce class wF(p,r,q) operators which is associated with Furuta inequality and generalized Aluthge transformation. Secondly, we shall show several properties of this class, such as its characterizations, inclusion relations, normality, powers and so on.In ChapterⅡ, we shall study classes of operators associated with Furuta inequality and Aluthge transformation, such as class F(p,r,q), class wF(p,r,q) and (p,r,q)-paranormal operators and so on.§2.1-§2.3 can be regarded as further discussion of§1.3 of ChapterⅠ.§2.4 is to show a characterization of p-hyponormal operators via class F(p, r, q) and (p, r, q)-paranormal operators.§2.5 is to discuss Aluthge transformation of p-hyponormal and log-hyponormal operators.