Strong Monotonicity of Spectral Radius of Positive Operators

Abstract

The classic result of Perron and Frobenius states that if $A$ and $B$ are matrices with nonnegative elements, such that $A\le B$, $A$ is irreducible, and $\rho (A)=\rho (B)$ then $A=B$. We extend this result to a large class of band irreducible positive operators on a large class of Banach lattices and provide examples to show that the conditions we put on operators and Banach lattices cannot be weakened.

References in corpus (1)

• Extensions of Perron-Frobenius Theory

Cited by in corpus (1)

• Extensions of Perron-Frobenius Theory