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Let G be a locally compact group with the left Haar measure m G and let A = a n , k n , k = 0 ∞ be a strongly regular matrix. We show that if μ is a power bounded measure on G, then there exists an idempotent measure θ μ such that w*- lim n → ∞ ∑ k = 0 ∞ a n , k μ k = θ μ. If μ is a probability measure on a compact group G, then w*- lim n → ∞ ∑ k = 0 ∞ a n , k μ k = m ¯ H , where H is the closed subgroup of G generated by supp μ and m ¯ H is the measure on G defined by m ¯ H E : = m H E ∩ H for every Borel subset E of G. [ABSTRACT FROM AUTHOR]

In this note, we present some results concerning intertwining properties of two isometries on Banach spaces. In this connection, we obtain also some Katznelson–Tzafriri type results for power bounded operators. [ABSTRACT FROM AUTHOR]

Let X be a complex Banach space and x ∈ X. Assume that a bounded linear operator T on X satisfies the condition e tT x ≤ C x 1 + t α α ≥ 0 , for all t ∈ R and for some constant C x > 0. For the function f from the Beurling algebra L ω 1 R with the weight ω t = 1 + t α , we can define an element in X, denoted by x f , which integrates e tT x with respect to f. We present a complete description of the elements x f in the case when the local spectrum of T at x consists of one point. In the case 0 ≤ α < 1 , some estimates for the norm of Tx via the local spectral radius of T at x are obtained. Some applications of these results are also given. [ABSTRACT FROM AUTHOR]

Let A be a complex commutative semisimple Banach algebra. In this paper, we study some ergodic properties of Cesàro bounded multipliers on A. The results are linked to the sets of synthesis and the main applications are concerned with Fourier and Fourier-Stieltjes algebras on locally compact groups. We study also the structure of ideals associated with multipliers of A and A-invariant projections of the dual space of A. Some related problems are also discussed. [ABSTRACT FROM AUTHOR]

Let A, T, and B be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences A n T B n and 1 n ∑ i = 0 n - 1 A i T B i . These results are applied to the Toeplitz, composition, and model operators. Some related problems are also discussed. [ABSTRACT FROM AUTHOR]