Norm-parallelism in classical M-ideals

In this paper, motivated by the results published by Zamani and Moslehian (2016), we study the relation of norm-parallelism for certain operators. The main aim of this paper is to give some characterizations of the norm-parallelism for bounded linear operators between Banach spaces. Further, we show that the notion of norm-parallelism may be related to the invariant subspace problem.