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中文摘要：
研究次范整线性空间上的可加奇性算子理论.引进可加奇性算子的三种不同的次范数和拟次范数,利用它们刻画可加奇性算子的三种有界性：有界、局部有界和球有界,深入讨论这三种有界性之间的关系,以及它们与连续性的关系.同时,还进一步研究次范整线性空间上连续可加奇性算子族的共鸣定理.
英文摘要：
The theory of additive odd operators on sub-normed integral-linear spaces is studied. Three different sub-norm and quasi-sub-norms of additive odd opera- tots on sub-normed integral-linear spaces are introduced. By using them, the three boundednesses of additive odd operators, i.e., boundedness, local-boundedness and ball-boundedness are characterized; the relations among the three boundednesses of additive odd operators and the relations between them and continuity are discussed in depth. At the same time, the resonance theorems about a family of continuous additive odd operators on sub-normed integral-linear spaces are further studied.
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