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Interpolating the Arithmetic-Geometric Mean Inequality and Its Operator Version

In: Advances in Matrix Inequalities

Author

Listed:
  • Mohammad Bagher Ghaemi

    (Iran University of Science and Technology)

  • Nahid Gharakhanlu

    (Iran University of Science and Technology)

  • Themistocles M. Rassias

    (National Technical University of Athens)

  • Reza Saadati

    (Iran University of Science and Technology)

Abstract

In this chapter, we gather refinements of the classical Young inequality for positive real numbers, and we use these refinements to establish improved Young and Heinz inequalities for operators. According to the definitions of operator entropies, relative operator entropies, and Tsallis operator entropy, the readers can employ the techniques in this chapter to get new upper and lower bounds of the operator entropies.

Suggested Citation

  • Mohammad Bagher Ghaemi & Nahid Gharakhanlu & Themistocles M. Rassias & Reza Saadati, 2021. "Interpolating the Arithmetic-Geometric Mean Inequality and Its Operator Version," Springer Optimization and Its Applications, in: Advances in Matrix Inequalities, chapter 0, pages 19-59, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-76047-2_2
    DOI: 10.1007/978-3-030-76047-2_2
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