Injective composition operators on Lorentz–Bochner spaces

In this paper, we extend the notion of essential range to vector-valued functions and present various equivalent conditions for the injectiveness of the composition operators alongwith a characterisation for measurable transformations inducing composition operators between Lorentz–Bochner spaces. Some aspects of the weighted composition operators on Lorentz–Bochner spaces, induced by a measurable transformation and an operator valued map, are also discussed.