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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

S-Numbers of Weighted Shift Operators on P-Summable Formal Entire Functions of M-Variables

Nashat Faried1, Z.A. Hassanain2, H. Abd El Ghaffar3 and A. Lokman3
  • 1 Ain Shams Universit, Egypt
  • 2 El-Gazeera High Institute for Engineering and Technology, Egypt
  • 3 Ain Shams University, Egypt

Abstract

The idea of multiplying a formal Taylor power series by z to make a right shift operator on the space of all square summable sequences of real numbers was due to A.L. Shield. In this work, we consider Taylor power series in m-variables and we give upper and lower estimations of s-numbers for multiplication of m- right weighted shift operators. This allowed us to estimate upper bounds for s-numbers of infinite series of m-right weighted shift operators and give some applications.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 79-85

DOI: https://doi.org/10.3844/jmssp.2019.79.85

Submitted On: 16 December 2018 Published On: 3 May 2019

How to Cite: Faried, N., Hassanain, Z., Abd El Ghaffar, H. & Lokman, A. (2019). S-Numbers of Weighted Shift Operators on P-Summable Formal Entire Functions of M-Variables. Journal of Mathematics and Statistics, 15(1), 79-85. https://doi.org/10.3844/jmssp.2019.79.85

Open AccessCopyright: © 2019 Nashat Faried, Z.A. Hassanain, H. Abd El Ghaffar and A. Lokman. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • S-Numbers
  • Shift Operators
  • Formal Power Series