In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilisti...In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilistic normed linear space was further studied. On probabilistic normed linear operator space, some resonance theorems dealing with probabilistic bounded sets, probabilistic semi_bounded sets, and probabilistic non_unbounded sets are obtained.展开更多
文摘In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilistic normed linear space was further studied. On probabilistic normed linear operator space, some resonance theorems dealing with probabilistic bounded sets, probabilistic semi_bounded sets, and probabilistic non_unbounded sets are obtained.
