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Approximate Birkhoff–James orthogonality and smoothness in the space of bounded linear operators

  • Arpita Mal
  • Kallol PaulEmail author
  • T. S. S. R. K. Rao
  • Debmalya Sain
Article
  • 15 Downloads

Abstract

We study approximate Birkhoff–James orthogonality of bounded linear operators defined between normed linear spaces \(\mathbb {X}\) and \(\mathbb {Y}.\) As an application of the results obtained, we characterize smoothness of a bounded linear operator T under the condition that \(\mathbb {K}(\mathbb {X},\mathbb {Y}),\) the space of compact linear operators is an M-ideal in \(\mathbb {L}(\mathbb {X},\mathbb {Y}),\) the space of bounded linear operators.

Keywords

Orthogonality Linear operators M-ideal L-ideal Smoothness 

Mathematics Subject Classification

Primary 46B28 Secondary 47L05 46B20 

Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia
  2. 2.Theoretical Statistics and Mathematics UnitIndian Statistical InstituteBengaluruIndia
  3. 3.Department of MathematicsIndian Institute of ScienceBengaluruIndia

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