Symmetry of Birkhoff-James Orthogonality of Bounded Linear Operators

  • Kallol Paul
  • Debmalya Sain
  • Puja Ghosh


We survey the recent developments in the study of symmetry of Birkhoff-James orthogonality of bounded linear operators between Banach spaces and Hilbert spaces. We also present some new results, along with the corresponding proofs, that have not been published before. In the last section we suggest some future directions for research, in particular connected to the notion of Ulam stability.


Birkhoff-James orthogonality Symmetry of orthogonality Bounded linear operators Ulam stability 

Mathematics Subject Classification (2010)

Primary 47L05; Secondary 46B20 39B82 



The authors gratefully acknowledge the contribution of Prof. J. Brzdek, specially in connection with the interrelation between Ulam stability and our research on symmetry of Birkhoff-James orthogonality which might open up the possibility of further research in this direction.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kallol Paul
    • 1
  • Debmalya Sain
    • 2
  • Puja Ghosh
    • 3
  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Department of MathematicsSabang Sajanikanta MahavidyalayaPaschim MedinipurIndia

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