We give a modified definition of a reproducing kernel Hilbert ⁎-module (shortly, ⁎) without using the condition of self-duality and discuss some related aspects; in particular, an interpolation theorem is presented. We investigate the exterior tensor product of ⁎s and find their reproducing kernel. In addition, we deal with left multipliers of ⁎s. Under some mild conditions, it is shown that one can make a new ⁎ via a left multiplier. Moreover, we introduce the Berezin transform of an operator in the context of ⁎s and construct a unital subalgebra of the unital ⁎-algebra consisting of adjointable maps on an ⁎ and show that it is closed with respect to a certain topology. Finally, the Papadakis theorem is extended to the setting of ⁎, and in order for the multiplication of two specific functions to be in the Papadakis ⁎, some conditions are explored.

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