The aim of this paper is to present a unified framework in the setting Hilbert $$C^*$$ -modules for scalar- and vector-valued reproducing kernel spaces -valued spaces. We investigate conditionally negative definite kernels with values -algebra adjointable operators acting on -module. In addition, we show that there exists two-sided connection between positive -modules. Furthermore, explore some...

Let M be a Banach C*-module over a C*-algebra A carrying two A-valued inner products 〈., .〉1, 〈., .〉2 which induce equivalent to the given one norms on M. Then the appropriate unital C*-algebras of adjointable bounded A-linear operators on the Hilbert A-modules {M, 〈., .〉1} and {M, 〈., .〉2} are shown to be ∗-isomorphic if and only if there exists a bounded A-linear isomorphism S of these two Hi...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.