Birkhoff-James orthogonality of operators in semi-Hilbertian spaces and its applications. (English) Zbl 1436.46017
The article under review explores the seminorm induced by a positive linear operator between Hilbert spaces. This consideration allows the author to consider a generalized version of Birkhoff-James orthogonality of operators on a Hilbert space, with respect to the corresponding semi-inner-product induced by the operator. The author obtains a Bhatia-Šemrl type characterization of orthogonality of linear operators, in the context of the above setting. Furthermore, some distance formulas have also been proved with respect to the said
seminorm.
Further study of the main idea developed in this article should be possible in case of some special classes of operators between Banach spaces.
Further study of the main idea developed in this article should be possible in case of some special classes of operators between Banach spaces.
Reviewer: Debmalya Sain (Contai)
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
| 46B28 | Spaces of operators; tensor products; approximation properties |
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