We present some properties of orthogonality and relate them with support disjoint and norm inequalities in $p-$Schatten ideals.In addition, we investigate the problem of characterization of norm--parallelism for bounded linear operators. We consider the characterization of norm--parallelism problem in $p-$Schatten ideals and locally uniformly convex spaces. Later on, we study the case when an operator is norm--parallel to the identity operator. Finally, we give some equivalence assertions about the norm--parallelism of compact operators. Some applications and generalizations are discussed for certain operators.

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