Birkhoff-James orthogonality in complex Banach spaces and Bhatia-Šemrl Theorem revisited

2021/09/27 by Roy, Saikat, Bagchi, Satya, Sain, Debmalya
#46B20 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A30 #Secondary 47A12

paper · doi:10.48550/arxiv.2109.12775

Abstract

We explore Birkhoff-James orthogonality of two elements in a complex Banach space by using the directional approach. Our investigation illustrates the geometric distinctions between a smooth point and a non-smooth point in a complex Banach space. As a concrete outcome of our study, we obtain a new proof of the Bhatia-Šemrl Theorem on orthogonality of linear operators.

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