Relationship among semi-bounded operators bounded operators and continuous operators

We show the definition of a new operator called semi-bounded operator in the topological linear space.We mainly study the relationships among semi-bounded operators,bounded operators and continuous operators.We proved if E is a locally bounded or locally convex topological linear space,E1 is a locally convex topological linear space,and T:E→E1,then T is a bounded operator if and only if T is a semi-bounded operator.Moreover,if E with axiom A1 is a locally bounded or locally convex topological linear space,E1 is a locally convex topological linear space,and,T:E→E1 is linear,then T is a continuous operator if and only if T is a semi-bounded operator.