Marcoux, Laurent W.Radjavi, HeydarZhang, Yuanhang2022-05-092022-05-092020-05-25https://doi.org/10.4064/sm190819-13-2http://hdl.handle.net/10012/18245Submission of a paper to Studia Mathematica implies that the work described therein has not been published before (except in the form of a preprint), that it is not under consideration for publication elsewhere, and that it will not be submitted elsewhere unless it has been rejected by the editors of Studia Mathematica. On the proof stage, the author will be asked to sign the copyright transfer agreement.Let H be a complex, separable Hilbert space, and B(H) denote the set of all bounded linear operators on H. Given an orthogonal projection P∈B(H) and an operator D∈B(H), we may write D=[D1D3D2D4] relative to the decomposition H=ranP⊕ran(I−P). In this paper we study the question: for which non-negative integers j, k can we find a normal operator D and an orthogonal projection P such that rank D2=j and rank D3=k? Complete results are obtained in the case where dimH<∞, and partial results are obtained in the infinite-dimensional setting.enbounded linear operatorsorthogonal projectionnon-negative integersinfinite-dimensional settingArticle