Skip to main content

Matrix transformations and generators of analytic semigroups

Abstract

We establish a relation between the notion of an operator of an analytic semigroup and matrix transformations mapping from a set of sequences into, where is either of the sets,, or. We get extensions of some results given by Labbas and de Malafosse concerning applications of the sum of operators in the nondifferential case.

[12345678910111213141516171819]

References

  1. 1.

    Altay B, Başar F: On the fine spectrum of the generalized difference operatorover the sequence spacesand. International Journal of Mathematics and Mathematical Sciences 2005,2005(18):3005–3013. 10.1155/IJMMS.2005.3005

    Article  MATH  MathSciNet  Google Scholar 

  2. 2.

    Da Prato G, Grisvard P: Sommes d'opérateurs linéaires et équations différentielles opérationnelles. Journal de Mathématiques Pures et Appliquées. Neuvième Série 1975,54(3):305–387.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    de Malafosse B: Some properties of the Cesàro operator in the space. Faculty of Sciences. University of Ankara. Series A1. Mathematics and Statistics 1999,48(1–2):53–71 (2000).

    MathSciNet  MATH  Google Scholar 

  4. 4.

    de Malafosse B: Application of the sum of operators in the commutative case to the infinite matrix theory. Soochow Journal of Mathematics 2001,27(4):405–421.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    de Malafosse B: Properties of some sets of sequences and application to the spaces of bounded difference sequences of order. Hokkaido Mathematical Journal 2002,31(2):283–299.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    de Malafosse B: On matrix transformations and sequence spaces. Rendiconti del Circolo Matematico di Palermo. Serie II 2003,52(2):189–210. 10.1007/BF02872228

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    de Malafosse B: On some BK spaces. International Journal of Mathematics and Mathematical Sciences 2003,2003(28):1783–1801. 10.1155/S0161171203204324

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    de Malafosse B: On the sets of sequences that are strongly-bounded and-convergent to naught with index. Seminario Matematico. Universitàe Politecnico di Torino 2003,61(1):13–32.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    de Malafosse B: The Banach algebra, whereis a BK space and applications. Matematichki Vesnik 2005,57(1–2):41–60.

    MathSciNet  MATH  Google Scholar 

  10. 10.

    de Malafosse B, Rakocevic V: Applications of measure of noncompactness in operators on the spaces,,and. to appear in Journal of Mathematical Analysis and Applications to appear in Journal of Mathematical Analysis and Applications

  11. 11.

    Fuhrman M: Sums of operators of parabolic type in a Hilbert space: strict solutions and maximal regularity. Advances in Mathematical Sciences and Applications 1994,4(1):1–34.

    MathSciNet  MATH  Google Scholar 

  12. 12.

    Grisvard P: Commutativité de deux foncteurs d'interpolation et applications. Journal de Mathématiques Pures et Appliquées. Neuvième Série 1966, 45: 143–206.

    MathSciNet  MATH  Google Scholar 

  13. 13.

    Jarrah AM, Malkowsky E: Ordinary, absolute and strong summability and matrix transformations. Filomat 2003,2003(17):59–78.

    MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Kato T: Perturbation Theory for Linear Operators, Die Grundlehren der mathematischen Wissenschaften. Volume 132. Springer, New York; 1966:xix+592.

    Google Scholar 

  15. 15.

    Labbas R, de Malafosse B: An application of the sum of linear operators in infinite matrix theory. Faculty of Sciences. University of Ankara. Series A1. Mathematics and Statistics 1997,46(1–2):191–210 (1998).

    MathSciNet  MATH  Google Scholar 

  16. 16.

    Labbas R, Terreni B: Somme d'opérateurs linéaires de type parabolique. I. Bollettino. Unione Matematica Italiana. B. Serie VII 1987,1(2):545–569.

    MathSciNet  MATH  Google Scholar 

  17. 17.

    Labbas R, Terreni B: Sommes d'opérateurs de type elliptique et parabolique. II. Applications. Bollettino. Unione Matematica Italiana. B. Serie VII 1988,2(1):141–162.

    MathSciNet  MATH  Google Scholar 

  18. 18.

    Pazy A: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences. Volume 44. Springer, New York; 1983:viii+279.

    Google Scholar 

  19. 19.

    Wilansky A: Summability Through Functional Analysis, North-Holland Mathematics Studies. Volume 85. North-Holland, Amsterdam; 1984:xii+318.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Bruno de Malafosse.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

de Malafosse, B., Medeghri, A. Matrix transformations and generators of analytic semigroups. J Inequal Appl 2006, 67062 (2006). https://doi.org/10.1155/JIA/2006/67062

Download citation

Keywords

  • Matrix Transformation
  • Analytic Semigroup
\