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Birkhoff–James Orthogonality and Geometry of Operator Spaces
Arpita Mal, Debmalya Sain, Kallol Paul, et al.
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Naturwissenschaften, Medizin, Informatik, Technik / Analysis
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.
Kundenbewertungen
Right Symmetric Operator, Birkhoff-James Orthogonality, Hilbert Space, Operator Norm Attainment, Left Symmetric Operator, Smoothness of an Operator, Bounded Linear Operator, Banach Space, k-smoothness of an Operator, Approximate Birkhoff-James Orthogonality, Extreme Contraction