Orthogonality and parallelism of operators on various Banach spaces
  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. 
T. Bottazzi, C. Conde, M. S. Moslehian, P. Wojcik and A. Zamani
math.FA