# Journal of Operator Theory

Volume 85, Issue 2, Spring 2021 pp. 463-474.

Birkhoff--James orthogonality to a subspace of operators defined between Banach spaces**Authors**: Arpita Mal (1), Kallol Paul (2)

**Author institution:**(1) Department of Mathematics, Jadavpur University, Kolkata, 700032, India

(2) Department of Mathematics, Jadavpur University, Kolkata, 700032, India

**Summary:**This paper deals with the study of Birkhoff--James orthogonality of a linear operator to a subspace of operators defined between arbitrary Banach spaces. In case the domain space is reflexive and the subspace is finite dimensional we obtain a complete characterization. For arbitrary Banach spaces, we obtain the same under some additional conditions. For an arbitrary Hilbert space $ \mathbb{H},$ we also study orthogonality to a subspace of the space of linear operators $\mathbb{L}(\mathbb{H}), $ both with respect to operator norm as well as numerical radius norm.

**DOI:**http://dx.doi.org/10.7900/jot.2019nov12.2262

**Keywords:**Birkhoff-James orthogonality, linear operators, subspace, numerical radius

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