Banach空间中带扰动的m-增生算子的零点与映象定理

ZEROS AND MAPPING THEOREMS FOR PERTURBATIONS OF m-ACCRETIVE OPERATORS IN BANACH SPACES

设 Ｘ为实 Ｂａｎａｃｈ空间，为 ｍ－增生算子，为有界算子（未必连续），而Ｃ（Ｔ＋Ｉ）－１为紧算子．假设，使得．则．进一步假设为强增生的，而Ｃ为闭的，则，其中Ｂｒ表示中心在原点半径为ｒ的开球．作为上述零点定理的应用，当Ｔ，Ｃ为奇算子时，我们获得一些新的映象定理．

Let X be a real Banach space and let T: X be an m-accretive operator. Let be a bounded operator (not necessarily continuous) such that is compact. Suppose that for every Jx such that Then we have. Assume, furthermore, that is strongly accretive, then, where Br(O) denotes the open ball of X with centre at zero and radius r > 0. As applications of the above zero theorem, we deduce many new mapping theorems. When T and C are odd operators, we also obtain some new mapping theorems.