In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be in...In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be infinite dimensional Banach spaces over complex field A. Denote by Y} the set of all bounded linear operators from X to Y. If X=Y, we write instead of B(X, F). For T^B(X"), let -D(T), ker T, R(T} denote the domain, kerner and the range of T respectively. For a subset MdX, M denotes the closure of M. Let H be a Hilbert space and MdH, then ML denotes the annihilator of If.展开更多
文摘In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be infinite dimensional Banach spaces over complex field A. Denote by Y} the set of all bounded linear operators from X to Y. If X=Y, we write instead of B(X, F). For T^B(X"), let -D(T), ker T, R(T} denote the domain, kerner and the range of T respectively. For a subset MdX, M denotes the closure of M. Let H be a Hilbert space and MdH, then ML denotes the annihilator of If.
