Approximate Birkhoff–James orthogonality in the space of bounded linear operators

Kallol Paul,Debmalya Sain,Arpita Mal

doi:10.1016/j.laa.2017.10.008

Approximate Birkhoff–James orthogonality in the space of bounded linear operators

Kallol Paul, Debmalya Sain + Show 1 more

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https://doi.org/10.1016/j.laa.2017.10.008

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Journal: Linear Algebra and Its Applications	Publication Date: Oct 17, 2017
Citations: 16	License type: publisher-specific-oa

Affiliation: Jadavpur University, Indian Institute of Science Bangalore

#Finite Dimensional Hilbert Space #Normed Space + Show 8 more

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Abstract

There are two notions of approximate Birkhoff–James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff–James orthogonality in the space of bounded linear operators defined on a normed space. A complete characterization of approximate Birkhoff–James orthogonality in the space of bounded linear operators defined on Hilbert space of any dimension is obtained which improves on the recent result by Chmieliński et al. (2017) [4], in which they characterized approximate Birkhoff–James orthogonality of linear operators on finite dimensional Hilbert space and also of compact operators on any Hilbert space.

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