Hi. I read a paper in which the author uses the propetry that if $A$ is a submodule of a
Hilbert $C^\ast$ module ($C$ is a $C^*$ algebra) such that
$A^\bot=0$ then $A$ is dense. I don't know how to prove it since in a gneral Hilbert module over a $C^*$ algebra $(A^\bot)^\bot$ is greater than $Closure(A)$ and the standard Hilbert space proof does not work.
The paper in question is: UNBOUNDED OPERATORS ON HILBERT C∗-MODULES OVER C∗-ALGEBRAS OF COMPACT OPERATORS by Guljas you can find on the web.