Birkhoff-James Orthogonality Of The Operators On A Hilbert Space

In this thesis,we study the Birkhoff-James orthogonality of bounded linear operators on a Hilbert space.Firstly,we give serval equivalent conditions about Birkhoff-James orthog-onality and strong Birkhoff-James orthogonality of bounded linear operators on a Hilbert space.Secondly,we discuss the relationship between isosceles orthogonality and Birkhoff-James orthogonality.Finally,we study the Birkhoff-James orthogonality of projections on a Hilbert space and obtain some interesting results.