Inequalities for the Schattenp-norm. IV

Springer Science and Business Media LLC - Tập 106 - Trang 581-585 - 1986
Fuad Kittaneh1
1Department of Mathematics, United Arab Emirates University, Al-Ain, United Arab Emirates

Tóm tắt

We prove some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA,B, andX are operators such thatA +B ≧ |X| andA +B ≧ |X*|, then ∥AX +XB∥ p p + ∥AX* +X*B∥ p p ≧2 ∥X∥ 2 2 for 1 ≦p<∞, and max (∥AX +XB∥, ∥AX* +X*B∥) ≧ ∥X∥2. Also, for any three operatorsA,B, andX, $$|| |A|X - X|B| ||_2^2 + || |A*|X - X|B*| ||_2^2 \leqq ||AX - XB||_2^2 + ||A*X - XB*||_2^2 .$$

Tài liệu tham khảo

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