We give a modified definition of a reproducing kernel Hilbert $C^{⁎}$-module (shortly, $RKH{C}^{⁎}M$) 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 $RKH{C}^{⁎}M$s and find their reproducing kernel. In addition, we deal with left multipliers of $RKH{C}^{⁎}M$s. Under some mild conditions, it is shown that one can make a new $RKH{C}^{⁎}M$ via a left multiplier. Moreover, we introduce the Berezin transform of an operator in the context of $RKH{C}^{⁎}M$s and construct a unital subalgebra of the unital $C^{⁎}$-algebra consisting of adjointable maps on an $RKH{C}^{⁎}M$ and show that it is closed with respect to a certain topology. Finally, the Papadakis theorem is extended to the setting of $RKH{C}^{⁎}M$, and in order for the multiplication of two specific functions to be in the Papadakis $RKH{C}^{⁎}M$, some conditions are explored.

我们给出了再生核 Hilbert 的修改定义 $C^{⁎}$-模块（很快， $\mathrm{电阻}钾H{C}^{⁎}米$) 不使用自我二元性的条件，讨论一些相关的方面；特别是，提出了一个插值定理。我们研究的外部张量积$\mathrm{电阻}钾H{C}^{⁎}米$s 并找到它们的复制内核。此外，我们处理左乘数$\mathrm{电阻}钾H{C}^{⁎}米$s。在一些温和的条件下，表明可以制造一种新的$\mathrm{电阻}钾H{C}^{⁎}米$通过左乘法器。此外，我们在以下上下文中引入了算子的 Berezin 变换$\mathrm{电阻}钾H{C}^{⁎}米$s 并构造单位的单位子代数 $C^{⁎}$- 由可伴随映射组成的代数 $\mathrm{电阻}钾H{C}^{⁎}米$并证明它相对于某个拓扑是封闭的。最后，将 Papadakis 定理扩展到$\mathrm{电阻}钾H{C}^{⁎}米$，并且为了使两个特定函数的乘法在 Papadakis $\mathrm{电阻}钾H{C}^{⁎}米$，探索了一些条件。