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On Joint Functional Calculus for Ritt Operators

  • Parasar MohantyEmail author
  • Samya Kumar Ray
Article
  • 39 Downloads

Abstract

In this paper, we study joint functional calculus for commuting n-tuple of Ritt operators. We provide an equivalent characterisation of boundedness for joint functional calculus for Ritt operators on \(L^p\)-spaces, \(1< p<\infty ,\) where each of them admits a bounded functional calculus. We also investigate joint similarity problem for commuting n-tuple of Ritt operators. We get our results by proving a suitable multivariable transfer principle between sectorial and Ritt operators as well as an appropriate joint dilation result in a general setting.

Keywords

Bounded functional calculus Ritt operators Sectorial operators 

Mathematics Subject Classification

Primary 47A60 Secondary 47A20 

Notes

Acknowledgements

We are thankful to Prof. C. Le Merdy for exposing us to the theory of Ritt operators and suggesting the problem as well as many valuable discussions and suggestions during this work. We appreciate Sayantan Chakrabarty’s help in drawing the pictures.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of TechnologyKanpurIndia
  2. 2.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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