Bhatia, Rajendra; Kittaneh, Fuad Clarkson inequalities with several operators. (English) Zbl 1071.47011 Bull. Lond. Math. Soc. 36, No. 6, 820-832 (2004). The authors discuss four norm inequalities. These inequalities hold for the Schatten \(p\)-norm as well as symmetric or unitarily invariant norms, and are extensions of the classical inequalities of J. A. Clarkson for the Lebesgue spaces \(L_{p}\) [Trans. Am. Math. Soc. 40, 396–414 (1936; Zbl 0015.35604)]. One of the inequalities is also an extension of the inequality proven by O. Hirzallah and F. Kittaneh in [Pac. J. Math. 202, 363–369 (2002; Zbl 1054.47011)]. In addition, by a similar discussion, the authors obtain an extension of the results by T. Ando and X.-Z. Zhan [Math. Ann. 315, 771–780 (1999; Zbl 0941.47004)] to a norm inequality of \(n\)-tuple of operators. Lastly, the authors show a norm inequality which interpolates the four norm inequalities under consideration. Reviewer: Takeaki Yamazaki (Yokohama) Cited in 2 ReviewsCited in 25 Documents MSC: 47A30 Norms (inequalities, more than one norm, etc.) of linear operators 46B20 Geometry and structure of normed linear spaces Keywords:Clarkson inequalities; Schatten \(p\)-norm; symmetric norm; unitarily invariant norm; parallelogram law; convex function Citations:Zbl 0015.35604; Zbl 1054.47011; Zbl 0941.47004 PDFBibTeX XMLCite \textit{R. Bhatia} and \textit{F. Kittaneh}, Bull. Lond. Math. Soc. 36, No. 6, 820--832 (2004; Zbl 1071.47011) Full Text: DOI