Normal operators with highly incompatible off-diagonal corners
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Date
2020-05-25
Authors
Marcoux, Laurent W.
Radjavi, Heydar
Zhang, Yuanhang
Journal Title
Journal ISSN
Volume Title
Publisher
Polish Academy of Sciences
Abstract
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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Keywords
bounded linear operators, orthogonal projection, non-negative integers, infinite-dimensional setting