Study Of b-Hilbert Spaces And Some Classes Of Operators

In this work, we have studied some geometric properties of some linear spaces; n-normed spaces, generalized 2-inner product spaces and b-Hilbert spaces, where we have proved some basic properties. As well as, we have given some new concept of b-congruence classes in generalized 2-inner product space. In addition, we have introduced definitions of ~self-adjoint operators and ~ positive operators in b-Hilbert space. Moreover, we have showed some of their properties and the relation between them. Finally this research shows that there is a lot of works in this area, especially the studied kinds of operators.