Sur la convergence de polynômes \(P_ n(T)\). (On the convergence of the polynomials \(P_ n(T))\). (French) Zbl 0594.47031
Summary: We present a weak-convergence criterion for a sequence of polynomials \(P_ n(T)\), where T is a positive operator on a Banach lattice. An example of T with norm-unbounded Cesaro averages for which \(T^ n/n\) converges strongly to zero is given. We study also the uniform and a.s. convergence to zero.
Keywords:
weak-convergence criterion for a sequence of polynomials; positive operator on a Banach lattice; norm-unbounded Cesaro averagesReferences:
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