Positive-normal Operators

Abstract

In this paper, we study some properties of positive-normal operators. In particular, we show that every positive-normal operator has finite ascent (i.e., kerT = ker-T^(2)), a quasiaffine transform of a positive-normal operator also has finite ascent, the restriction of a positive-normal operator to an invariant subspace is still positive-normal, and the similarity does not preserve positive- normality.;이 논문에서는 positive-normal 작용소의 몇 가지 성질에 관하여 공부한다. 모든 positive-normal 작용소는 finite ascent를 가짐을 보이고 quasiaffine transform 역시 finite ascent를 가짐을 증명한다. 그리고 Positive-normal 작용소의 invariant subspace로의 제한이 여전히 positive-normal이며 similarity는 positive-normality를 보존하지 못한다는 것을 보인다.