Skip to main content
SpringerLink
Log in

Spectral mapping theorems for exponentially bounded c-semigroups in Banach spaces

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

LetZ be a generator of an exponentially boundedC-semigroup {S t } t≥0 in a Banach space and letT t =C −1 S t . We show that the spectral mapping theorems such as exp(tσ(Z)) ⊂ σ(T t ) and exp(tσ p (Z)) ⊂ tσ p (T t ) ⊂ exp(tσ p (Z)) ⋃ {0} for everyt≥0 hold.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. B. Davies and M. M. H. Pang,The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987), 181–208.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. A. Goldstein,Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.

    MATH  Google Scholar 

  3. I. Miyadera,On the generation of exponentially bounded semigroups, Proc. Jap. Acad. 62, Ser. A (1986), 239–242.

    MATH  MathSciNet  Google Scholar 

  4. I. Miyadera and N. Tanaka,Exponentially bounded C-semigroups and generation of semigroups, to appear.

  5. A. Pazy,Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.

    MATH  Google Scholar 

  6. N. Tanaka,On the exponentially bounded C-semigroups, to appear.

Download references

Author information

Authors and Affiliations

  1. Pusan National University, Pusan, Korea

    Ki Sik Ha

Authors
  1. Ki Sik Ha
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The present studies were supported by the Basic Science Research Institute Program, Ministry of Education, 1987.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ha, K.S. Spectral mapping theorems for exponentially bounded c-semigroups in Banach spaces. Semigroup Forum 38, 215–221 (1989). https://doi.org/10.1007/BF02573232

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02573232

Keywords

Search

Navigation