Aljoša Peperko

Inequalities on the spectral radius and the operator norm of Hadamard products of positive operators on sequence spaces

Relatively recently, K.M.R. Audenaert (2010), R.A. Horn and F. Zhang (2010), Z. Huang (2011), A.R. Schep (2011), A. Peperko (2012), D. Chen and Y. Zhang (2015) have proved inequalities on the spectral radius and the operator norm of Hadamard products and ordinary matrix products of finite and infinite non-negative matrices that define operators on sequence spaces. In the current paper we extend and refine several of these results and also prove some analogues for the numerical radius. Some inequalities seem to be new even in the case of

Inequalities on the spectral radius, operator norm and numerical radius of the Hadamard weighted geometric mean of positive kernel operators

n\times n

On the functional inequality for the spectral radius of compact operators

non-negative matrices.

Semigroups of max-plus linear operators

ABSTRACT Recently, several authors have proved inequalities on the spectral radius , operator norm and numerical radius of Hadamard products and ordinary products of nonnegative matrices that define operators on sequence spaces, or of the Hadamard geometric mean and ordinary products of positive kernel operators on Banach function spaces. In the present article we generalize and refine several of these results. In particular, we show that for a Hadamard geometric mean of positive kernel operators A and B on a Banach function space L, we have In the special case we also prove that

Lower spectral radius and spectral mapping theorem for suprema preserving mappings

Elsner et al. [Functional inequalities for spectral radii of nonnegative matrices, Linear Algebra Appl. 129 (1990), pp. 103–130] characterized functions satisfying for all non-negative matrices A 1, … , A n of the same order, where r denotes the spectral radius. We generalize this result to the setting of infinite non-negative matrices that define compact operators on a Banach sequence space.

Logarithmic convexity of fixed points of stochastic kernel operators

We define strongly continuous max-additive and max-plus linear operator semigroups and study their main properties. We present some important examples of such semigroups coming from non-linear evolution equations.

Inequalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators

We study Lipschitz, positively homogeneous and finite suprema preserving mappings defined on a max-cone of positive elements in a normed vector lattice. We prove that the lower spectral radius of such a mapping is always a minimum value of its approximate point spectrum. We apply this result to show that the spectral mapping theorem holds for the approximate point spectrum of such a mapping. By applying this spectral mapping theorem we obtain new inequalites for the Bonsall cone spectral radius of max type kernel operators.

Uniform Boundedness Principle for Nonlinear Operators on Cones of Functions

In this paper we prove results on logarithmic convexity of fixed points of stochastic kernel operators. These results are expected to play a key role in the economic application to strategic market games.

On the max version of the generalized spectral radius theorem

ABSTRACT Let Ψ and Σ be bounded sets of positive kernel operators on a Banach function space L. We prove several refinements of the known inequalities for the generalized spectral radius ρ and the joint spectral radius , where denotes the Hadamard (Schur) geometric mean of the sets Ψ and Σ. Furthermore, we prove that analogous inequalities hold also for the generalized essential spectral radius and the joint essential spectral radius in the case when L and its Banach dual have order continuous norms.

Inequalities for the hadamard weighted geometric mean of positive kernel operators on banach function spaces

We prove a uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous, and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically nonlinear operators.