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中文摘要：
给出在∑e^1型Banach空间中一致有界函半群的生成元是有界线性算子的若干充分条件．证明了在∑e^1型Banach空间中由Hermitian算子或由等距算子组成的函半群的生成元都是有界线性算子．证明了在∑e^1型Banach空间中每个强连续非拟解析余弦族的生成元必是有界线性算子．
英文摘要：
This paper gives some sufficient conditions for the generators of uniformly bounded C0-semigroups to be bounded linear oprators in ∑e^1 type Banach spaces; shows that the generator of C0-semigroup consisting of Hermitian operators or isometrics is always a bounded linear operator in such spaces; shows that the generator of strongly continuous non-quasianalytic cosine family is necessarily a bounded linear operator in such spaces.
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