SOME INEQUALITIES FOR UNITARILY INVARIANT NORMS

作者：Hu, Xingkai^*

来源：Journal of Mathematical Inequalities, 2012, 6(4): 615-623.

DOI：10.7153/jmi-06-59

• Unitarily invariant norms
• positive semidefinite matrices
• Cauchy-Schwarz inequality
• convex function
• Heinz inequality

This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality involving positive definite matrix and Hilbert-Schmidt norm. Then we use it to discuss the conjecture on the Hilbert-Schmidt norm of matrices proposed by Sloane and Harwit and the conjecture is proved for some special matrices.

• 出版日期2012-12
• 单位昆明理工大学