Spectral radius of operators associated with dynamical systems in the spaces C(X)
Krzysztof Zajkowski (2005)
Banach Center Publications
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We consider operators acting in the space C(X) (X is a compact topological space) of the form , u ∈ C(X), where and are given continuous mappings (1 ≤ k ≤ N). A new formula on the logarithm of the spectral radius r(A) is obtained. The logarithm of r(A) is defined as a nonlinear functional λ depending on the vector of functions . We prove that , where Mes is the set of all probability vectors of measures on X × 1,..., N and λ* is some convex lower-semicontinuous functional on...