Abstract
We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReA≧a≧0, then for any operatorX, ∥AX+XA*∥ p ≧2a∥X∥ p . Also, for any two operatorsA andB, ∥∣A∣−∣B∥ 22 +∥∣A*∣B*∣∥ 22 ≤2∥A−B∥ 22 .
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Araki, H., Yamagami, S.: An inequality for the Hilbert-Schmidt norm. Commun. Math. Phys.81, 89–96 (1981)
Gohberg, I.C., Krein, M.G.: Introduction to the theory of linear nonselfadjoint operators. Transl. Math. Monogr.18, Providence, R.I.: Am. Math. Soc. 1969
van Hemmen, J.L., Ando, T.: An inequality for trace ideals. Commun. Math. Phys.76, 143–148 (1980)
Kittaneh, F.: Inequalities for the Schattenp-norm. Glasgow Math. J.26, 141–143 (1985)
Kittaneh, F.: Inequalities for the Schattenp-norm. II. Glasgow Math. J. (to appear)
Kittaneh, F.: On Lipschitz functions of normal operators. Proc. Am. Math. Soc.94, 416–418 (1985)
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Communicated by H. Araki
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Kittaneh, F. Inequalities for the Schattenp-norm. III. Commun.Math. Phys. 104, 307–310 (1986). https://doi.org/10.1007/BF01211597
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DOI: https://doi.org/10.1007/BF01211597