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Some Remarks on the Matrix Domain and the Spectra of a Generalized Difference Operator

  • Laxmipriya NayakEmail author
Research Paper
  • 53 Downloads
Part of the following topical collections:
  1. Mathematics

Abstract

Recently, Meng and Mei (J Math Anal Appl, 2018. https://doi.org/10.1016/j.jmaa.2018.10.051) have introduced two Euler difference sequence spaces \(e_0^t(B_\nu ^{(m)})\) and \(e_c^t(B_\nu ^{(m)})\) using generalized difference operator \(B_\nu ^{(m)}\). Some functional properties and Köthe–Toeplitz duals of the proposed spaces have been determined. Also, the fine spectra of the generalized difference operator \(B_\nu ^{(m)}\) over the sequence space \(\ell _1\) have been computed following the results of Dutta and Baliarsingh (Appl Math Comput 219:1776–1784, 2012). In fact, the results for the spectra of the said difference operators are new and interesting. Upon further investigations, it has been noticed that these results should be improved and modified. The primary objective of this note is to provide such sorts of substantial modifications on these results.

Keywords

The difference operators \(\Delta _\nu ^{m}\) and \(B_\nu ^{(m)}\) Difference sequence spaces The spectrum of an operator 

Mathematics Subject Classification

47A10 40A05 46A45 

Notes

Compliance with Ethical Standards

Conflict of interest

The author declares that they have no conflict of interest.

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of Applied SciencesKIIT Deemed to be UniversityBhubaneswarIndia

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