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Results in Mathematics

, 74:41 | Cite as

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

  • Gholamreza TalebiEmail author
Article
  • 27 Downloads

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.

Keywords

Four-dimensional matrices double sequence space domain spaces of \(\mathcal {L}_p\) 

Mathematics Subject Classification

46A45 40G05 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of MathematicsVali-e-Asr University of RafsanjanRafsanjanIslamic Republic of Iran

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