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Some remarks on Birkhoff-James orthogonality of linear operators
TLDR
In this article, the authors studied the Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces and obtained a characterization of Euclidean spaces.Abstract:
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.read more
References
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Journal ArticleDOI
Orthogonality and linear functionals in normed linear spaces
TL;DR: The notion of orthogonality was introduced in this paper, which is a generalization of the notion of homogeneous homogeneous elements to normed linear spaces, and has been studied extensively in the literature.
Journal ArticleDOI
Semi-inner-product spaces
TL;DR: In this article, the authors propose a theory of semi-inner-product spaces for vector spaces on which instead of a bilinear form there is defined a form [x, y] which is linear in one component only, strictly positive, and satisfies a Schwarz inequality.
Journal ArticleDOI
Classes of semi-inner-product spaces
Journal ArticleDOI
Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces
TL;DR: In this paper, it was shown that T ∈ L ( l p 2 ) (p ≥ 2, p ≠ ∞ ) is left symmetric with respect to Birkhoff-James orthogonality if and only if T is the zero operator.
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