Given a Hilbert module E over a C*-algebra A, we show that the collection of
all bounded A-module operators acting on E forms the reflexive closure for the
algebra of the adjointable operators. We also make an observation regarding the
representation theory of the left centralizer algebra of a C*-algebra and use
it to give an intuitive proof of a related result of H. LinComment: The paper will appear in the Illinois J. Mat