×
Gao, Fugen; Li, Meng

Clarkson inequalities related to convex and concave functions. (English) Zbl 1500.47017

Math. Slovaca 71, No. 5, 1319-1327 (2021).
The authors obtain some norm inequalities involving convex and concave functions, which are the generalizations of the classical Clarkson inequalities. The techniques are standard and it seems that the results can be extended to the setting \(\tau\)-measurable operators; see [M. S. Moslehian and G. Sadeghi, Commun. Appl. Math. Comput. 28, No. 4, 379–389 (2014; Zbl 1324.47037)]].
Reviewer: Mohammad Sal Moslehian (Mashhad)

MSC:

47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
46B20 Geometry and structure of normed linear spaces

Keywords:

Clarkson inequalities; unitarily invariant norm; Schatten \(p\)-norm; convex function; concave function

Citations:

Zbl 1324.47037
Cite Review PDF
Full Text: DOI

References:

[1] Alrimawi, F.—Hirzallah, O.—Kittaneh, F.: Norm inequalities involving convex and concave functions of operators, Linear Multilinear Algebra 67 (2019), 1757-1772. · Zbl 07089815
[2] Aujla, J.—Silva, F.: Weak majorization inequalities and convex functions, Linear Algebra Appl. 369 (2003), 217-233. · Zbl 1031.47007
[3] Bhatia, R.: Matrix Analysis, Springer-Verlag, New York, 1997.
[4] Bhatia, R.—Holbrook, J.: On the Clarkson-McCarthy inequalities, Math. Ann. 281 (1988), 7-12. · Zbl 0618.47008
[5] Bhatia, R.—Kittaneh, F.: Clarkson inequalities with several operators, Bull. London Math. Soc. 36 (2004), 820-832. · Zbl 1071.47011
[6] Bourin, J. C.—Uchiyama, M.: A matrix subadditivity inequality for f(A + B) and f(A) + f(B), Linear Algebra Appl. 423 (2007), 512-518. · Zbl 1123.15013
[7] Fack, T.—Kosaki, H.: Generalized s-numbers of τ-measurable operators, Pacific J. Math. 123 (1986), 269-300. · Zbl 0617.46063
[8] Formisano, T.—Kissin, E.: Clarkson-McCarthy inequalities for ℓ_p spaces of operators in Schatten ideals, Integral Equ. Oper. Theory 79 (2014), 151-173. · Zbl 1310.46016
[9] Gohberg, I. C.—Krein, M. G.: Introduction to the Theory of Linear Nonselfadjoint Operators. Transl. Math. Monographs 18, Amer. Math. Soc. Providence, RI, 1969. · Zbl 0181.13503
[10] Gumus, I. H.—Hirzallah, O.—Kittaneh, F.: Eigenvalue localization for complex matrices, Electron. J. Linear Algebra 27 (2014), 892-906. · Zbl 1326.15015
[11] Gumus, I. H.—Hirzallah, O.—Kittaneh, F.: Estimates for the real and imaginary parts of the eigenvalues of matrices and applications, Linear Multilinear Algebra 36 (2016), 2431-2445. · Zbl 1361.15021
[12] Hirzallah, O.—Kittaneh, F.: Non-commutative Clarkson inequalities for unitarily invariant norms, Pacific J. Math. 202 (2002), 363-369. · Zbl 1054.47011
[13] Hirzallah, O.—Kittaneh, F.: Non-commutative Clarkson inequalities for n-tuples of operator, Integral Equ. Oper. Theory 60(3) (2008), 369-379. · Zbl 1155.47013
[14] Kissin, E.: On Clarkson-McCarthy inequalities for n-tuples of operators, Proc. Amer. Math. Soc. 135 (2007), 2483-2495. · Zbl 1140.47005
[15] Kosem, T.: Inequalities between ∣f(A + B)∣ and ∣f(A) + f(B)∣, Linear Algebra Appl. 418 (2006), 153-160. · Zbl 1105.15016
[16] McCarthy, C. A.: c_p, Isr. J. Math. 5 (1967), 249-271. · Zbl 0156.37902
[17] Simon, B.: Trace Ideals and their Applications, Cambridge University Press, Cambridge, 1979. · Zbl 0423.47001
[18] Uchiyama, M.: Subadditivity of eigenvalue sums, Proc. Amer. Math. Soc. 134 (2006), 1405-1412. · Zbl 1089.47010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.