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Abstract We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-Semrl property. We first prove that every functional on a Banach space X has the Bhatia-Semrl property… Click to show full abstract
Abstract We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-Semrl property. We first prove that every functional on a Banach space X has the Bhatia-Semrl property if and only if X is reflexive. We also find some geometric conditions of Banach space which ensure the denseness of operators with Bhatia-Semrl property. Finally, we investigate operators with the Bhatia-Semrl property when a domain space is L 1 [ 0 , 1 ] or C [ 0 , 1 ] .
Keywords:
semrl property;
bhatia semrl;
birkhoff james;
james orthogonality
Journal Title: Linear Algebra and its Applications
Year Published: 2019
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Journal Title: Linear Algebra and its Applications
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!