Some Basic Theorems for Linear OperatorsBetween Fuzzy Normed Spaces

Some basic properties for linear operators between fuzzy normed spaces are further studied. Firstly, the concepts of openness, closedness, ρ-openness and ρ-closedness of operators are introduced, and at the same time, the relations among them are discussed. Moreover, by making use of these concepts, a certain number of theorems are established, including the open mapping theorem, the semi-open mapping theorem, the closed graph theorem, the semi-closed graph theorem, the bounded inverse theorem and the semi-bounded inverse theorem. Finally, some applications related to these theorems are given.