∑e1型Banach空间中某些C0半群和余弦族的生成元的连续性

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

∑_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

(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

(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/Abstract

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 ∑_e¹type 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

苏维钢, 钟怀杰. ∑_e¹型Banach空间中某些C₀半群和余弦族的生成元的连续性[J]. 数学物理学报, 2009, 29(2): 392-398.

SU Wei-Gang, ZHONG Fu-Jie. Continuity for the Generators of some C₀-semigroups and Cosine Families |in ∑_e¹ Type Banach Spaces[J]. Acta mathematica scientia,Series A, 2009, 29(2): 392-398.

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∑_e¹型Banach空间中某些C₀半群和余弦族的生成元的连续性

Continuity for the Generators of some C₀-semigroups and Cosine Families |in ∑_e¹ Type Banach Spaces

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