03596nam a22005655i 4500 978-981-99-7111-4 DE-He213 20251030111432.0 cr nn 008mamaa 240219s2024 si | s |||| 0|eng d 9789819971114 978-981-99-7111-4 10.1007/978-981-99-7111-4 doi QA329-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Mal, Arpita. author. aut http://id.loc.gov/vocabulary/relators/aut 71301 Birkhoff–James Orthogonality and Geometry of Operator Spaces [electronic resource] / by Arpita Mal, Kallol Paul, Debmalya Sain. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. XIII, 251 p. 13 illus., 4 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Infosys Science Foundation Series in Mathematical Sciences, 2364-4044 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. 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. Operator theory. 71302 Geometry. 68763 Functional analysis. 71303 Operator Theory. 71304 Geometry. 68763 Functional Analysis. 71305 Paul, Kallol. author. aut http://id.loc.gov/vocabulary/relators/aut 71306 Sain, Debmalya. author. (orcid)0000-0002-9721-1597 https://orcid.org/0000-0002-9721-1597 aut http://id.loc.gov/vocabulary/relators/aut 71307 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819971107 Printed edition: 9789819971121 Printed edition: 9789819971138 Infosys Science Foundation Series in Mathematical Sciences, 2364-4044 69688 https://doi.org/10.1007/978-981-99-7111-4 ZDB-2-SMA ZDB-2-SXMS 57719 57719