Orthogonality and Numerical radius inequalities of operator matrices

Abstract

We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of numerical radius for $n\times n$ operator matrices, which improve on and generalize existing lower bounds. We also obtain a better lower bound of numerical radius for an upper triangular operator matrix.

References in corpus (5)

• Cartesian decomposition and Numerical radius inequalities
• Numerical radius inequalities and its applications in estimation of zeros of polynomials
• Birkhoff-James orthogonality and smoothness of bounded linear operators
• On some geometric properties of operator spaces
• Orthogonality of matrices in the Ky Fan $k$-norms

Cited by in corpus (3)

• Improved inequalities for the numerical radius via Cartesian decomposition
• Numerical radius inequalities for tensor product of operators
• An extension of Birkhoff--James orthogonality relations in semi-Hilbertian space operators