Monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations

2024/08/08 by Bogdanović, Katarina, Peperko, Aljoša
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2408.04357

Abstract

We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on L². To our knowledge, several proved properties are new even in the finite dimensional case.

Related

• Inequalities on the essential joint and essential generalized spectral radius
• Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators
• Hadamard weighted geometric mean inequalities for the spectral and essential spectral radius of positive operators on Banach function and sequence spaces
• Strong Monotonicity of Spectral Radius of Positive Operators
• Inequalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators