Mal, Arpita. creator author. aut http://id.loc.gov/vocabulary/relators/aut Paul, Kallol. author. aut http://id.loc.gov/vocabulary/relators/aut Sain, Debmalya. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text si 2024 1st ed. 2024. monographic eng

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electronic resource

access XIII, 251 p. 13 illus., 4 illus. in color. online resource. This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of Birkhoff–James orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces. 1 Notations and Terminologies -- 2 Basic theory of B-J orthogonality in Banach space -- 3 Operator norm attainment -- 4 B-J orthogonality of operators -- 5 Approximate B-J orthogonality -- 6 Smoothness and k−smoothness of operators -- 7 Symmetry of the B-J orthogonality -- 8 Extreme contractions. by Arpita Mal, Kallol Paul, Debmalya Sain. Operator theory Geometry Functional analysis Operator Theory Geometry Functional Analysis QA329-329.9 9789819971114 https://doi.org/10.1007/978-981-99-7111-4 https://doi.org/10.1007/978-981-99-7111-4 240219 20251030111432.0 978-981-99-7111-4