Advances in Operator Theory

Orthogonality of bounded linear operators on complex Banach spaces

Kallol Paul, ‎Debmalya Sain, ‎Arpita Mal, and Kalidas Mandal

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‎We study Birkhoff-James orthogonality of compact linear operators on complex reflexive Banach spaces and obtain its characterization‎. ‎By means of introducing new definitions‎, ‎we illustrate that it is possible in the complex case‎, ‎to develop a study of orthogonality of compact linear operators‎, ‎analogous to the real case‎. ‎Furthermore‎, ‎earlier operator theoretic characterizations of Birkhoff-James orthogonality in the real case‎, ‎can be obtained as simple corollaries to our present study‎. ‎In fact‎, ‎we obtain more than one equivalent characterizations of Birkhoff-James orthogonality of compact linear operators in the complex case‎, ‎in order to distinguish the complex case from the real case‎.

Article information

Adv. Oper. Theory, Volume 3, Number 3 (2018), 699-709.

Received: 1 December 2017
Accepted: 11 March 2018
First available in Project Euclid: 4 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]

Birkhoff-James orthogonality ‎complex Banach space ‎bounded linear operator


Paul, Kallol; Sain, ‎Debmalya; Mal, ‎Arpita; Mandal, Kalidas. Orthogonality of bounded linear operators on complex Banach spaces. Adv. Oper. Theory 3 (2018), no. 3, 699--709. doi:10.15352/aot.1712-1268.

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