Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (2): 392-398.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 46B26
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