LAUSR

We introduce and study modular Birkhoff–James orthogonality for typical Banach modules $$B({\mathbb {X}},{\mathbb {Y}})$$ and $$K({\mathbb {X}},{\mathbb {Y}}),$$ where $${\mathbb {X}}$$ and $${\mathbb {Y}}$$ are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in $$B({\mathbb {X}},{\mathbb {Y}})$$ and $$K({\mathbb {X}},{\mathbb {Y}}).$$ The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.