OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
Abstract
Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥A|ran P is said to be an off-diagonal corner of A, and L is said to be essential if ∩{ker L : L ∈ L} = {0} and ∩{ker L ∗ : L ∈ L} = {0}, where L ∗ denotes the adjoint of L. Our goal in this paper is to determine effective upper bounds on dim A in terms of dim L, where L is an essential off-diagonal corner of A. A detailed structure analysis of A based upon the dimension of L, while seemingly elusive in general, is nevertheless provided in the cases where dim L ∈ {1, 2}.
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Cite this version of the work
Laurent W. Marcoux, Heydar Radjavi, Yuanhang Zhang
(2020).
OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn). UWSpace.
http://hdl.handle.net/10012/18254
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