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Some refinements of young type inequality for positive linear map

  • Chaojun Yang , Yaxin Gao and Fangyan Lu EMAIL logo
Published/Copyright: July 19, 2019
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 69 Issue 4

Abstract

We obtain a refined Young type inequality in this paper. The conclusion is presented as follows: Let A, B ∈ B(𝓗) be two positive operators and p ∈ [0, 1], then

A♯pB+G∗(A♯pB)G≤A∇pB−2r(A∇B−A♯B),

where r = min{p, 1 – p}, G = L(2p)2A–1S(A|B), L(t) is periodic with period one and L(t) = t221−tt2t for t ∈ [0, 1]. Moreover, we give the s-th powering of two inequalities related to the above one with s > 0 which refines Lin’s work. In the mean time, we present an inequality involving Hilbert-Schmidt norm.

MSC 2010: Primary 47A63; Secondary 46B20
Keywords: Young inequality; positive linear map; Kantorovich constant; arithmetic-geometric means

The research was supported by NNSFC (No. 11571247).

  1. (Communicated by Werner Timmermann)

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Received: 2018-05-24
Accepted: 2018-11-02
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0277
Keywords for this article
Young inequality; positive linear map; Kantorovich constant; arithmetic-geometric means

Articles in the same Issue

  1. Regular papers
  2. On the finite embeddability property for quantum B-algebras
  3. A dual Ramsey theorem for finite ordered oriented graphs
  4. On EMV-Semirings
  5. A nonsymmetrical matrix and its factorizations
  6. On weakly 𝓗-permutable subgroups of finite groups
  7. The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions
  8. A geometrical version of Hardy-Rellich type inequalities
  9. On a Choquet-Stieltjes type integral on intervals
  10. Uniqueness of meromorphic functions sharing four small functions on annuli
  11. A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
  12. Functions of bounded variation related to domains bounded by conic sections
  13. Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables
  14. Oscillatory criteria for the second order linear ordinary differential equations
  15. When deviation happens between rough statistical convergence and rough weighted statistical convergence
  16. The retraction of certain banach right modules associated to a character
  17. On sequence spaces generated by binomial difference operator of fractional order
  18. Some refinements of young type inequality for positive linear map
  19. On the Gromov-Hausdorff limit of metric spaces
  20. The beta exponentiated Nadarajah-Haghighi distribution: theory, regression model and application
  21. Hilbert algebras with supremum generated by finite chains
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