Birkhoff--James orthogonality to a subspace of operators defined between Banach spaces

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 H, we also study orthogonality to a subspace of the space of linear operators L(H), both with respect to operator norm as well as numerical radius norm.