Certain types of linear operators on probabilistic Hilbert space

The purpose of this paper is to introduce some definitions, properties and basic results that show the relation between F-bounded of linear operator in probabilistic Hilbert space and bounded operator in norm. In the paper, we prove that the adjoint operator in probabilistic Hilbert space is bounded. The notion of the continuous operators in probabilistic Hilbert space and some basic results are given. In addition, we note that every operator in probabilistic real Hilbert space is a self-adjoint Operator.