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Original Articles

On norm sub-additivity and super-additivity inequalities for concave and convex functions

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Pages 1369-1389 | Received 10 Dec 2010, Accepted 21 Dec 2011, Published online: 16 Feb 2012

References

  • Ando , T . 1988 . Comparison of norms ||| f(A) − f(B)||| and ||| f(|A − B|)||| . Math. Z. , 197 : 403 – 409 .
  • Ando , T and Zhan , X . 1999 . Norm inequalities related to operator monotone functions . Math. Ann. , 315 : 771 – 780 .
  • Aujla , JS . 2000 . Some norm inequalities for completely monotone functions . SIAM J. Matrix Anal. Appl. , 22 : 569 – 573 .
  • Aujla , JS and Bourin , J-C . 2007 . Eigenvalue inequalities for convex and log-convex functions . Linear Algebra Appl. , 424 : 25 – 35 .
  • Aujla , JS and Silva , FC . 2003 . Weak majorization inequalities and convex functions . Linear Algebra Appl. , 369 : 217 – 233 .
  • Bhatia , R . 1987 . Some inequalities for norm ideals . Commun. Math. Phys. , 111 : 33 – 39 .
  • Bhatia , R . 1997 . Matrix Analysis , Heidelberg : Springer .
  • Bhatia , R and Kittaneh , F . 1998 . Norm inequalities for positive operators . Lett. Math. Phys. , 43 : 225 – 231 .
  • Birman , MSh , Koplienko , LS and Solomyak , MZ . 1975 . Estimates of the spectrum of the difference between fractional powers of self-adjoint operators . Izv. Vyssh. Uchebn. Zaved. Mat. , 19 : 3 – 10 .
  • Bourin , J-C and Uchiyama , M . 2007 . A matrix subadditivity inequality for f(A + B) and f(A) + f(B) . Linear Algebra Appl. , 423 : 512 – 518 .
  • Hiai , F . 1997 . Log-majorizations and norm inequalities for exponential operators . Banach Center Publ. , 38 : 119 – 181 .
  • Hille , E and Philips , RS . 1957 . Functional Analysis and Semi-groups, AMS Colloquium Publications , Vol. 31 , Providence, RI : AMS .
  • Hiriart-Urruty , J-B and Ye , D . 1995 . Sensitivity analysis of all eigenvalues of a symmetric matrix . Numer. Math. , 70 : 45 – 72 .
  • Horn , RA and Johnson , CR . 1985 . Matrix Analysis , Cambridge : Cambridge University Press .
  • Kato , T . 1995 . Perturbation Theory for Linear Operators, Reprint of the 1980 edition , Berlin : Classics in Mathematics, Springer-Verlag .
  • Kittaneh , F . 1986 . Inequalities for Schatten p-norm IV . Commun. Math. Phys. , 106 : 581 – 585 .
  • Kittaneh , F and Kosaki , H . 1987 . Inequalities for Schatten p-norm V . Publ. Res. Inst. Math. Sci. , 23 : 433 – 443 .
  • Kosem , T . 2006 . Inequalities between || f(A + B)|| and || f(A) + f(B)|| . Linear Algebra Appl. , 418 : 153 – 160 .
  • Mathias , R . 1990 . Concavity of monotone matrix functions of finite order . Linear Multilinear Algebra , 27 : 129 – 138 .
  • McCarthy , CA . 1967 . c p . Israel J. Math. , 5 : 249 – 271 .
  • Overton , ML and Womersley , RS . 1993 . Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices . Math. Program. Ser. B , 62 : 321 – 357 .
  • Powers , RT and Størmer , E . 1970 . Free states of the canonical anticommutator relations . Commun. Math. Phys. , 16 : 1 – 33 .

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