On Mappings Approximately Preserving a Particular Value of Inner Product
Kong Lian · Journal of Shangluo University · 2014
In complex Hilbert spaces, the definition of mapping approximately preserving a particular value of the inner product is given. Then the properties of linear mapping approximately preserving a particular value of the inner product are studied. Finally, it is proved that the nonzero linear mapping approximately preserving a particular value of the inner product is bounded and bounded below by parallelogram law. The result is a generalization of approximate orthogonality preserving linear mappings.