2018/10/11 by Sain, Debmalya, Paul, Kallol, Mal, Arpita
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 47L05 #Secondary 46B20
paper · doi:10.48550/arxiv.1810.04845
We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and improve some of the recent results in this context. In particular, we obtain a characterization of Euclidean spaces and also prove that it is possible to retrieve the norm of a compact (bounded) linear operator (functional) in terms of its Birkhoff-James orthogonality set. We also present some best approximation type results in the space of bounded linear operators.