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Improved Young and Heinz operator inequalities for unitarily invariant norms

  • A. Beiranvand and Amir Ghasem Ghazanfari EMAIL logo
Published/Copyright: March 10, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 2

Abstract

In this paper, we present numerous refinements of the Young inequality by the Kantorovich constant. We use these improved inequalities to establish corresponding operator inequalities on a Hilbert space and some new inequalities involving the Hilbert-Schmidt norm of matrices. We also give some refinements of the following Heron type inequality for unitarily invariant norm |||⋅||| and A, B, X ∈ Mn(ℂ):

|||AνXB1−ν+A1−νXBν2|||≤(4r0−1)|||A12XB12|||+2(1−2r0)|||(1−α)A12XB12+α(AX+XB2)|||,

where 14≤ν≤34,α∈[12,∞) and r0 = min{ν, 1 – ν}.

MSC 2010: Primary 47A63; 47A64
Keywords: Operator inequalities; Young inequality; Heinz mean; Kantorovich constant

  1. Communicated by Gregor Dolinar

Acknowledgement

The authors would like to express their thanks to referees for careful reading and kind suggestion.

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Received: 2018-11-08
Accepted: 2019-09-24
Published Online: 2020-03-10
Published in Print: 2020-04-28

© 2020 Mathematical Institute Slovak Academy of Sciences

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  1. Regular papers
  2. Relatively residuated lattices and posets
  3. Strongly s-dense injective hull and Banaschewski’s theorems for acts
  4. Wild sets in global function fields
  5. Generators and integral points on elliptic curves associated with simplest quartic fields
  6. New Filbert and Lilbert matrices with asymmetric entries
  7. Returning functions with closed graph are continuous
  8. On sets of points of approximate continuity and ϱ-upper continuity
  9. Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
  10. On solvability of some nonlocal boundary value problems for biharmonic equation
  11. The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
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  15. Sequences of positive homoclinic solutions to difference equations with variable exponent
  16. Modified Lupaş-Jain operators
  17. New fixed point results in bv(s)-metric spaces
  18. Improved Young and Heinz operator inequalities for unitarily invariant norms
  19. Scrutiny of some fixed point results by S-operators without triangular inequality
  20. The lattices of families of regular sets in topological spaces
  21. Iterated partial summations applied to finite-support discrete distributions
  22. Hamiltonicity of a class of toroidal graphs
https://doi.org/10.1515/ms-2017-0363
Keywords for this article
Operator inequalities; Young inequality; Heinz mean; Kantorovich constant

Articles in the same Issue

  1. Regular papers
  2. Relatively residuated lattices and posets
  3. Strongly s-dense injective hull and Banaschewski’s theorems for acts
  4. Wild sets in global function fields
  5. Generators and integral points on elliptic curves associated with simplest quartic fields
  6. New Filbert and Lilbert matrices with asymmetric entries
  7. Returning functions with closed graph are continuous
  8. On sets of points of approximate continuity and ϱ-upper continuity
  9. Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
  10. On solvability of some nonlocal boundary value problems for biharmonic equation
  11. The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
  12. Strongly increasing solutions of higher-order quasilinear ordinary differential equations
  13. Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
  14. Filippov solutions of vector Dirichlet problems
  15. Sequences of positive homoclinic solutions to difference equations with variable exponent
  16. Modified Lupaş-Jain operators
  17. New fixed point results in bv(s)-metric spaces
  18. Improved Young and Heinz operator inequalities for unitarily invariant norms
  19. Scrutiny of some fixed point results by S-operators without triangular inequality
  20. The lattices of families of regular sets in topological spaces
  21. Iterated partial summations applied to finite-support discrete distributions
  22. Hamiltonicity of a class of toroidal graphs
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