In this paper, we investigate a type of perturbation of angle in Hilbert C*-modules. When a vector x makes approximate angle θ with a vector y, for some θ ∈ 0, π, we look for another vector w, close enough to the vector y, so that x makes the exact angle θ with w. This problem has been recently studied for orthogonality by some authors in normed spaces. We have been able to develop the method for angles in the setting of Hilbert C*-module. We first consider the problem in inner product spaces, and prove some results in this regard. Then, we try to extend it to some classes of normed spaces such as Hilbert C+-modules and B(H), the algebra of all bounded linear operators on a Hilbert space H.
Behdani et al. (Wed,) studied this question.