数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 392-398.

• 论文 • 上一篇    下一篇

e1型Banach空间中某些C0半群和余弦族的生成元的连续性

苏维钢, 钟怀杰   

  1. (福建师范大学数学与计算机科学学院 |福州 350007)
  • 收稿日期:2007-11-08 修回日期:2008-09-07 出版日期:2009-04-25 发布日期:2009-04-25
  • 基金资助:

    国家自然科学基金(10771034, 10471025)、福建省自然科学基金(Z0511019)资助

Continuity for the Generators of some C0-semigroups and Cosine Families |in ∑e1 Type Banach Spaces

 SU Wei-Gang, ZHONG Fu-Jie   

  1. (School of Mathematics and Computer Science,  Fujian Normal University, Fuzhou 350007)
  • Received:2007-11-08 Revised:2008-09-07 Online:2009-04-25 Published:2009-04-25

摘要:

给出在∑e1型Banach空间中一致有界C0半群的生成元是有界线性算子的若干充分条件. 证明了在∑e1型Banach空间中 由Hermitian算子或由等距算子组成的C0半群的生成元都是有界线性算子.证明了在∑e1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.

关键词: e1型空间, C0半群, 余弦族, 生成元

Abstract:

This paper gives some sufficient conditions for the generators of uniformly bounded C0-semigroups to be bounded linear oprators in  ∑e1 type Banach spaces;  shows that the generator of  C0-semigroup  consisting of Hermitian operators or  isometries 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.

Key words: e1 type space, C0-semigroup, Cosine family, Generator

中图分类号: 

  • 46B26