Normal operators with highly incompatible off-diagonal corners
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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.
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Laurent W. Marcoux, Heydar Radjavi, Yuanhang Zhang (2020). Normal operators with highly incompatible off-diagonal corners. UWSpace. http://hdl.handle.net/10012/18245