  This paper deals with 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 arbitrary Hilbert space $
\mathbb{H},$ we also study orthogonality to subspace of the space of linear
operators $L(\mathbb{H}), $ both with respect to operator norm as well as
numerical radius norm.
