zbMATH — the first resource for mathematics

Clarkson inequalities with several operators. (English) Zbl 1071.47011
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.

47A30 Norms (inequalities, more than one norm, etc.) of linear operators
46B20 Geometry and structure of normed linear spaces
Full Text: DOI