Positivity

, Volume 22, Issue 2, pp 575–586 | Cite as

On Cesàro summability of vector valued multiplier spaces and operator valued series

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Abstract

In this paper, we introduce and study vector valued multiplier spaces with the help of the sequence of continuous linear operators between normed spaces and Cesàro convergence. Also, we obtain a new version of the Orlicz–Pettis Theorem by means of Cesàro summability.

Keywords

Multiplier convergent series Cesàro sequence spaces Summing operator Compact operators Orlicz–Pettis theorem 

Mathematics Subject Classification

Primary: 46B15 Secondary: 40A05 46B45 

Notes

Acknowledgements

The authors wish to thank the referee for his/her valuable suggestions, which improved the paper considerably.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of EducationInonu UniversityMalatyaTurkey
  2. 2.Department of MathematicsSiirt UniversitySiirtTurkey

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