Bhatia, Rajendra; Holbrook, John A. R. On the Clarkson-McCarthy inequalities. (English) Zbl 0618.47008 Math. Ann. 281, No. 1, 7-12 (1988). Some famous inequalities of McCarthy for Schatten p-norms of Hilbert space operators are interpreted in such a way that a much easier proof and an extension to a wider class of norms become possible. Cited in 1 ReviewCited in 15 Documents 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.) Keywords:inequalities; Schatten p-norms of Hilbert space operators PDF BibTeX XML Cite \textit{R. Bhatia} and \textit{J. A. R. Holbrook}, Math. Ann. 281, No. 1, 7--12 (1988; Zbl 0618.47008) Full Text: DOI EuDML References: [1] Ando, T.: Majorisation, doubly stochastic matrices and comparison of eigenvalues. Lecture Notes, Sapporo, 1982. Linear Algebra Appl. (to appear) · Zbl 0484.15017 [2] Bhatia, R.: Some inequalities for norm ideals. Commun. Math. Phys.111, 33-39 (1987) · Zbl 0632.47005 · doi:10.1007/BF01239013 [3] Bhatia, R., Holbrook, J.A.R.: Unitary invariance and spectral variation. Linear Algebra Appl.95, 43-68 (1987) · Zbl 0657.15019 · doi:10.1016/0024-3795(87)90026-7 [4] Donoghue, W.: Monotone matrix functions and analytic continuation. Berlin, Heidelberg, New York: Springer 1974 · Zbl 0278.30004 [5] Gohberg, I.C., Krein, M.G.: Introduction to the theory of linear nonselfadjoint operators Am. Math. Soc. Translations of Mathematical Monographs, Vol. 18 (1969) · Zbl 0181.13504 [6] Marshall, A.W., Olkin, I.: Inequalities: Theory of majorisation and its applications. New York: Academic Press 1979 · Zbl 0437.26007 [7] McCarthy, C.A.:c p . Isr. J. Math.5, 249-271 (1967) · Zbl 0156.37902 · doi:10.1007/BF02771613 [8] Phillips, J.: Generalised Powers-Størmer inequalities. Talk at the Canadian Operator Theory Conference, Victoria, July 1986 (unpublished) [9] Powers, R.T., Størmer, E.: Free states of the canonical anticommutation relations. Commun. Math. Phys.16, 1-33 (1970) · Zbl 0186.28301 · doi:10.1007/BF01645492 [10] Schatten, R.: Norm ideals of completely continuous operators (Sec. Ed.). Berlin, Heidelberg, New York: Springer 1970 · Zbl 0188.44103 [11] Simon, B.: Trace ideals and their applications. Cambridge University Press, 1979 · Zbl 0423.47001 [12] Thompson, R.C.: Convex and concave functions of singular values of matrix sums. Pac. J. Math.62, 285-290 (1976) · Zbl 0361.15014 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.