New semi-norm of semi-Hilbertian space operators and its application

Abstract

In this paper, we introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for it. As an application of this new semi-norm, we obtain upper bounds for the A-numerical radius of semi-Hilbertian space operators, which are sharper than the earlier ones.

References in corpus (5)

• Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
• Proper improvement of well-known numerical radius inequalities and their applications
• On inequalities for A-numerical radius of operators
• On a new norm on $\mathcal{B}(\mathcal{H})$ and its applications to numerical radius inequalities
• Numerical radius inequalities of operator matrices from a new norm on $\mathcal{B}(\mathcal{H})$

Cited by in corpus (1)

• Generalized $A$-numerical radius of operators and related inequalities