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A study of orthogonality of bounded linear operators

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Abstract

We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced by us and also discuss some of the possible applications in this regard. We also study isosceles orthogonality of bounded (positive) linear operators on a Hilbert space and some of the related properties, including that of operators having disjoint support. We further explore the relations between Birkhoff-James orthogonality and isosceles orthogonality in a general Banach space.

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Acknowledgements

The research of Dr. Tamara Bottazzi and Dr. Cristian Conde is partially supported by National Scientific and Technical Resesarch Conuncil of Argentina (CONICET) and ANPCyT PICT 2017-2522. The research of Dr. Debmalya Sain is sponsored by Dr. D. S. Kothari Post-doctoral Fellowship, under the mentorship of Professor Gadadhar Misra. Dr. Sain feels elated to acknowledge the wonderful hospitality of the lovely couple Mr. Subhro Jana and Mrs. Poulomi Mallik.

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Authors and Affiliations

  1. Universidad Nacional de Río Negro, LaPAC, Sede Andina (8400), S.C. de Bariloche, Argentina

    Tamara Bottazzi

  2. Consejo Nacional de Investigaciones Científicas y Técnicas CONICET, Buenos Aires, Argentina

    Tamara Bottazzi

  3. Instituto Argentino de Matemática “Alberto Calderón”, Saavedra 15 3er. piso, (C1083ACA), Buenos Aires, Argentina

    Cristian Conde

  4. Instituto de Ciencias, Universidad Nacional de Gral. Sarmiento, J. M. Gutierrez 1150, (B1613GSX), Los Polvorines, Argentina

    Cristian Conde

  5. Indian Institute of Science, Bengaluru, Karnataka, India

    Debmalya Sain

Authors
  1. Tamara Bottazzi
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  2. Cristian Conde
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  3. Debmalya Sain
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Corresponding author

Correspondence to Cristian Conde.

Additional information

Communicated by Fuad Kittaneh.

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Bottazzi, T., Conde, C. & Sain, D. A study of orthogonality of bounded linear operators. Banach J. Math. Anal. 14, 1001–1018 (2020). https://doi.org/10.1007/s43037-019-00050-0

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  • DOI: https://doi.org/10.1007/s43037-019-00050-0

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