Numerical Radius Inequalities Concerning with Algebra Norms

Abstract

We present an expression for the generalized numerical radius associated with a norm on the algebra of bounded linear operators on a Hilbert space and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities involving the product of two operators. Applications of our inequalities are also provided.

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Acknowledgements

The authors would like to thank the referee for her/his valuable suggestions and comments. Ali Zamani is supported by the Science and Technology Commission of Shanghai Municipality (18590745200), Mohammad Sal Moslehian (corresponding author) is supported from a Grant from Ferdowsi University of Mashhad (No. 2/52244), and Qingxiang Xu is supported by the National Natural Science Foundation of China (11671261, 11971136).

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Correspondence to Mohammad Sal Moslehian.

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Zamani, A., Moslehian, M.S., Xu, Q. et al. Numerical Radius Inequalities Concerning with Algebra Norms. Mediterr. J. Math. 18, 38 (2021). https://doi.org/10.1007/s00009-020-01665-6

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Keywords

  • Numerical radius
  • operator norm
  • inequality
  • Cartesian decomposition

Mathematics Subject Classification

  • Primary 47A12
  • Secondary 47A30