Zagreb Workshop on Operator Theory

On orthogonality preserving mappings on Hilbert C^*-modules

Recent results on various characterizations of orthogonality of elements and of orthogonality preserving mappings on Hilbert C*-modules will be compared. Some new results can be explained. The still open conjecture by Lj. Arambasic and R. Rajic whether the orthogonality of two elements x and y of a certain Hilbert C*-module is equivalent to the condition that |x| <= |x+ty| for any complex number t is brought down to a much simpler situation in atomic von Neumann factors in the possible affirmative case. Some results are joint work with M. S. Moslehian and A. Zamani.