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Birkhoff-James Orthogonality and geometry of operator spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Birkhoff-James Orthogonality and geometry of operator spacesby Arpita Mal, Kallol Paul, Debmalya Sain.
Author:	Mal, Arpita.
other author:	Paul, Kallol.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	xiii, 251 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Operator theory.
Online resource:	https://doi.org/10.1007/978-981-99-7111-4
ISBN:	9789819971114$q(electronic bk.)

Birkhoff-James Orthogonality and geometry of operator spaces
Mal, Arpita.

Birkhoff-James Orthogonality and geometry of operator spaces[electronic resource] /by Arpita Mal, Kallol Paul, Debmalya Sain. - Singapore :Springer Nature Singapore :2024. - xiii, 251 p. :ill., digital ;24 cm. - Infosys science foundation series in mathematical sciences,2364-4044. - Infosys science foundation series in mathematical sciences..

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.

ISBN: 9789819971114$q(electronic bk.)

Standard No.: 10.1007/978-981-99-7111-4doiSubjects--Topical Terms:

229156
Operator theory.

LC Class. No.: QA329

Dewey Class. No.: 515.724

Birkhoff-James Orthogonality and geometry of operator spaces
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505 0 $a 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.
520 $a 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.
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