Annals of Functional Analysis

Young type inequalities for positive operators

Cristian Conde

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In this paper we present refinements and improvement of the Young inequality in the context of linear bounded‎ ‎operators‎.

Article information

Ann. Funct. Anal. Volume 4, Number 2 (2013), 144-152.

First available in Project Euclid: 12 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 47A30‎ 15A6

Young inequality Heinz inequality ‎Positive operators ‎unitarily invariant norm


Conde, Cristian. Young type inequalities for positive operators. Ann. Funct. Anal. 4 (2013), no. 2, 144--152. doi:10.15352/afa/1399899532.

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  • T. Ando, Matrix Young inequalities, Oper. Theory Adv. Appl. 75 (1995), 33–38.
  • R. Bhatia and C. Davis, More matrix forms of the arithmatic–geometric mean inequality, SIAM J. Matrix Anal. Appl. 14 (1993) 132–136.
  • R. Bhatia, Positive Definite Matrices, Princeton University Press, New Jersey, 2007.
  • R. Kaur, M.S. Moslehian, M. Singh and C. Conde, Further Refinements of Heinz Inequality, Linear Algbera Appl. (2013),
  • L. Galvani, Sulle funzioni converse di una o due variabili definite in aggregate qualunque, Rend. Circ. Mat. Palermo 41 (1916), 103–134.
  • E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung. (German), Math. Ann. 123 (1951), 415–438.
  • F. Hiai and H. Kosaki, Means for matrices and comparison of their norms, Indiana Univ. Math. J. 48 (1999) 899–936.
  • F. Hiai and H. Kosaki, Comparison of various means for operators, J. Funct. Anal. 163 (1999), 300–323.
  • F. Hiai and H. Kosaki, Means of Hilbert space operators, Lecture notes in Mathematics 1820, Springer, New York, 2003.
  • H. Kober, On the arithmetic and geometric means and on Hölder's inequality, Proc. Amer. Math. Soc. 9 1958 452–459.
  • H. Kosaki, Arithmetic–geometric mean and related inequalities for operators, J. Funct. Anal. 156 (1998), 429–451.
  • F. Kittaneh, Norm inequalities for fractional powers of positive operators, Lett. Math. Phys. 27 (1993), no. 4, 279–285.
  • F. Kittaneh, On convexity of the Heinz Means, Integral Equations Operator Theory 68 (2010) 519–527.
  • F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrices, J. Math. Anal. Appl. 361 (2010), no. 1, 262–269.
  • A. McIntosh, Heinz inequalities and perturbation of spectral families, Macquarie Mathematical Reports, Macquarie Univ., 1979.
  • N. Minculete, A refinement of the Kittaneh–Manasrah inequality, Creat. Math. Inform. 20 (2011), no. 2, 157–162.
  • M.S. Moslehian, M. Tominaga and K.-S. Saito, Schatten $p$-norm inequalities related to an extended operator parallelogram law, Linear Algebra Appl. 435 (2011), no. 4, 823–829.
  • C. Niculescu and L.-E. Persson, Convex functions and their applications. A contemporary approach, CMS Books in Mathematics/Ouvrages de Mathmatiques de la SMC, 23. Springer, New York, 2006.
  • T. Yamazaki, Characterizations of $\log A\geq\log B$ and normaloid operators via Heinz inequality, Integral Equations Operator Theory 43 (2002), no. 2, 237–247.