Öz
Kaynakça
- [1] T. Ando and F. Hiai, Log-majorization and complementary Golden–Thompson type inequalities, Linear Alg. Appl. 197/198, 113–131, 1994.
- [2] T. Ando and F. Hiai, Operator log-convex functions and operator means, Math. Ann. 350 (3), 611–630, 2011.
- [3] T. Ando and X. Zhan, Norm inequalities related to operator monotone functions, Math. Ann. 315, 771–780, 1999.
- [4] R. Bhatia, Matrix analysis, Springer-Verlag, New York, 1997.
- [5] J.C. Bourin and M. Uchiyama, A matrix subadditivity inequality for $f (A+B)$ and $f (A)+ f (B)$, Linear Algebra Appl. 423, 512–518, 2007.
- [6] T. Furuta, J. Micic Hot, J. Pecaric and Y. Seo, Mond-Pecaric Method in Operator Inequalities, Monographs in Inequalities 1, Element, Zagreb, 2005.
- [7] F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246, 205-224, 1980.
- [8] M. Lin, On an operator Kantorovich inequality for positive linear maps, J. Math. Anal. Appl. 402, 127–132, 2013.
- [9] J. Mićić, Z. Pavić and J. Pečarić, Jensen’s inequality for operators without operator convexity, Linear Algebra Appl. 434, 1228–1237, 2011.
- [10] H.R. Moradi, Z. Heydarbeygi and M. Sababheh, Subadditive inequalities for operators, Math. Ineq. Appl. 23 (1), 317–327, 2020.
- [11] R. Nakamoto and M. Nakamura, Operator mean and Kantorovich inequality, Math. Japon. 44 (3), 495–498, 1996.
- [12] M. Uchiyama, Operator monotone functions, positive definite kernels and majorization, Proc. Amer. Math. Soc. 138 (11), 3985–3996, 2010.
Öz
The main goal of this article is to show that many inequalities that are not valid in operator theory become true if we add a separation condition on the spectra. The applications include showing how monotone functions behave like operator monotone functions and how the Choi-Davis inequality becomes valid for convex functions under this separation condition.
Anahtar Kelimeler
Operator order separated spectra convex functions operator monotone functions
Kaynakça
- [1] T. Ando and F. Hiai, Log-majorization and complementary Golden–Thompson type inequalities, Linear Alg. Appl. 197/198, 113–131, 1994.
- [2] T. Ando and F. Hiai, Operator log-convex functions and operator means, Math. Ann. 350 (3), 611–630, 2011.
- [3] T. Ando and X. Zhan, Norm inequalities related to operator monotone functions, Math. Ann. 315, 771–780, 1999.
- [4] R. Bhatia, Matrix analysis, Springer-Verlag, New York, 1997.
- [5] J.C. Bourin and M. Uchiyama, A matrix subadditivity inequality for $f (A+B)$ and $f (A)+ f (B)$, Linear Algebra Appl. 423, 512–518, 2007.
- [6] T. Furuta, J. Micic Hot, J. Pecaric and Y. Seo, Mond-Pecaric Method in Operator Inequalities, Monographs in Inequalities 1, Element, Zagreb, 2005.
- [7] F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246, 205-224, 1980.
- [8] M. Lin, On an operator Kantorovich inequality for positive linear maps, J. Math. Anal. Appl. 402, 127–132, 2013.
- [9] J. Mićić, Z. Pavić and J. Pečarić, Jensen’s inequality for operators without operator convexity, Linear Algebra Appl. 434, 1228–1237, 2011.
- [10] H.R. Moradi, Z. Heydarbeygi and M. Sababheh, Subadditive inequalities for operators, Math. Ineq. Appl. 23 (1), 317–327, 2020.
- [11] R. Nakamoto and M. Nakamura, Operator mean and Kantorovich inequality, Math. Japon. 44 (3), 495–498, 1996.
- [12] M. Uchiyama, Operator monotone functions, positive definite kernels and majorization, Proc. Amer. Math. Soc. 138 (11), 3985–3996, 2010.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 6 Ağustos 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 50 Sayı: 4 |