Birkhoff–James Orthogonality and Geometry of Operator Spaces
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Beschreibung
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.
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.
Analyzes the norm structure through algebraic approaches with geometric visualization Focuses on topics in geometry of operator spaces through Birkhoff–James orthogonality Covers a vast area of geometric notions in the space of bounded linear operators
Autor*in
Arpita Mal
Themen in »Birkhoff–James Orthogonality and Geometry of Operator Spaces«
Hilbert Space Banach Space Birkhoff-James Orthogonality Smoothness of an Operator k-smoothness of an Operator Bounded Linear Operator Approximate Birkhoff-James Orthogonality Extreme Contraction Right Symmetric Operator Operator Norm Attainment Left Symmetric Operator
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“This interesting book deals with various ramifications of the geometric notion of Birkhoff-James orthogonality in both concrete and abstract situations. … this well-written monograph is a must-read for anyone interested in aspects of Birkhoff-James orthogonality and its interplay with the geometry of Banach spaces.” (T.S.S.R.K. Rao, zbMATH 1547.46002, 2024)
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