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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.

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