SOME NEW NUMERICAL RADIUS AND HILBERT-SCHMIDT NUMERICAL RADIUS INEQUALITIES FOR HILBERT SPACE OPERATORS

In this article, we give new upper and lower bounds of numerical radius and Hilbert-Schmidt numerical radius inequalities for Hilbert space operators. In particular, we show that if X is an element of C-2 with the Cartesian decomposition X = A+ iB, then 1/4 parallel to|X|(2) +|X*|(2)parallel to(2) <= 1/root 2 omega(2) ([(B2) (0) (0) (A2)]) <= omega(2)(2) (X). This is an analog of Kittaneh in [Studia Math. 168 (2005): 73-80].

Automated summary

In this article, new upper and lower bounds of numerical radius and Hilbert-Schmidt numerical radius inequalities for Hilbert space operators are presented. Specifically, it is shown that if X is an element of C-2 with the Cartesian decomposition X = A+ iB, then 1/4||X||(2) +||X*||(2)parallel(2) <= 1/root 2 ω(2) ([(B2) (0) (0) (A2)]) <= ω(2)(2) (X). This result is an analog of Kittaneh in [Studia Math. 168 (2005): 73-80].