Gene

Quantum mechanics

Spectral radius

Operator norm

Diagonal

Banach space

Product (mathematics)

Inequality

Pure mathematics

Materials science

Operator matrix

Computer security

RADIUS

Diagonal matrix

Eigenvalues and eigenvectors

Hilbert space

Biochemistry

Computer science

Matrix (chemical analysis)

Physics

Upper and lower bounds

Mathematics

Transcription factor

Mathematical analysis

Geometry

Composite material

Combinatorics

Repressor

Chemistry

Operator (biology)

Quasinormal operator

Algebra over a field

Multiplication operator

Finite-rank operator

Linear and Multilinear Algebra

We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of n×n operator matrices by using non-negative continuous functions on [0,∞). We also obtain some upper and lower bounds for the B-numerical radius of operator matrices, where B is the diagonal operator matrix whose each diagonal entry is a positive operator A. We show that these bounds generalize and improve on the existing bounds.

Some improvements of numerical radius inequalities of operators and operator matrices