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Boundedness Problem of Four-Dimensional Matrices on the Domain Spaces of \(\mathcal {L}_p\)

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Abstract

In this paper, we introduce and study the domain of an arbitrary four-dimensional summability matrix in the double sequence space \(\mathcal {L}_p\) and focus on the boundedness problem of four-dimensional operators on it. We consider the class of four-dimensional Hausdorff matrices as operators mapping \(\mathcal {L}_p\) into these domains and provide a Hardy type formula for their operator norms and lower bounds. Then we apply our results to some special domains of \(\mathcal {L}_p\) such as the double Laurent, Taylor and Euler sequence spaces. Finally, we provide a general upper estimate for the operator norms of four-dimensional matrices which have real and complex entries with certain conditions.

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References

  1. Başar, F., Sever, Y.: The space \(\cal{L}_p\) of double sequences. Math. J. Okayama Univ. 51, 149–157 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Mursaleen, M., Başar, F.: Domain of Cesáro mean of order one in some spaces of double sequences. Stud. Sci. Math. Hungar. 51(3), 335–356 (2014)

    MATH  Google Scholar 

  3. Rhoades, B.E.: Some classes of doubly infinite matrices. Indian J. Pure Appl. Math. 23(6), 419–427 (2003)

    MathSciNet  MATH  Google Scholar 

  4. Talebi, G.: On boundedness of four-dimensional Hausdorff matrices on the double Taylor sequence spaces. Indag. Math. 28(5), 953–961 (2017)

    Article  MathSciNet  Google Scholar 

  5. Talebi, G.: Operator norm and lower bound of four-dimensional matrices. Indag. Math. 28(6), 1134–1143 (2017)

    Article  MathSciNet  Google Scholar 

  6. Talebi, G.: Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces. Linear Multilinear Algebra 65(11), 2257–2267 (2017)

    Article  MathSciNet  Google Scholar 

  7. Talebi, G.: Complementary results on the boundedness problem of factorizable four-dimensional matrices. Bull. Malays. Math. Sci. Soc. (2018). https://doi.org/10.1007/s40840-018-00703-7

  8. Talebi, G.: Lower bound of four-dimensional Hausdorff matrices, preprint

  9. Tuğ, O., Başar, F.: Four-dimensional generalized difference matrix and some double sequence spaces, In AIP Conference Proceedings, vol. 1759, No. 1, p. 020075. AIP Publishing, New york

  10. Tuğ, O.: Four-dimensional generalized difference matrix and some double sequence spaces. J. Inequal. Appl. 2017, 149 (2017). https://doi.org/10.1186/s13660-017-1423-y

    Article  MathSciNet  MATH  Google Scholar 

  11. Yeşilkayagil, M., Başar, F.: Mercerian theorem for four-dimensional matrices. Commun. Fac. Sci. Univ. Ankara, Ser. A1 Math. Stat. 65(1), 147–155 (2016)

    MathSciNet  MATH  Google Scholar 

  12. Yeşilkayagil, M., Başar, F.: On the characterization of some classes of four-dimensional matrices and Steinhaus type theorems. Kragujevac J. Math. 40(1), 35–45 (2016)

    Article  MathSciNet  Google Scholar 

  13. Yeşilkayagil, M., Başar, F.: Four-dimensional dual and dual of the new sort summability methods. Contemp. Anal. Appl. Math. 3(1), 13–29 (2015)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran

    Gholamreza Talebi

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  1. Gholamreza Talebi
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Correspondence to Gholamreza Talebi.

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The paper is dedicated to Hazrat Bibi Fatimah Zahra, the leader of all the women of the world for all times, on the occasion of the 1429th anniversary of her martyrdom

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Talebi, G. Boundedness Problem of Four-Dimensional Matrices on the Domain Spaces of \(\mathcal {L}_p\). Results Math 74, 41 (2019). https://doi.org/10.1007/s00025-019-0958-2

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  • DOI: https://doi.org/10.1007/s00025-019-0958-2

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