• Corpus ID: 224710735

New Estimates on the bounds of Brunel's operator.

  title={New Estimates on the bounds of Brunel's operator.},
  author={Idris Assani and R. Spencer Hallyburton and Sebastien McMahon and Stefano Schmidt and Cornelis Jan Schoone},
  journal={arXiv: Dynamical Systems},
We study the coefficients of the Taylor series expansion of powers of the function $\psi(x)=\frac{1-\sqrt{1-x}}{x}$, where Brunel's operator $A$ is defined as $\psi(T)$. The operator $A$ was shown to map positive mean-bounded (and power-bounded) operators to positive power-bounded operators. We provide specific details of results announced by A. Brunel and R. Emilion in \cite{Brunel}. In particular, we sharpen an estimate to prove that $\sup_{n\in\mathbb{N}} \|n(A^n-A^{n+1})\| < \infty$. We… 

Figures from this paper




Every one of the important strong limit theorems that we have seen thus far – the strong law of large numbers, the martingale convergence theorem, and the ergodic theorem – has relied in a crucial

Théorème ergodique ponctuel pour un semi-groupe commutatif finiment engendré de contractions de $L^1$

© Gauthier-Villars, 1973, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section B » (http://www.elsevier.com/locate/anihpb) implique l’accord avec les conditions

On discrete subordination of power bounded and Ritt operators

It is shown that (infinite) convex combinations of powers of Ritt operators are Ritt, which is a unified framework for several main results on discrete subordination from [19] and answer a question left open in [19].

Subordinated discrete semigroups of operators

Given a power-bounded linear operator T in a Banach space and a probability F on the non-negative integers, one can form a 'subordinated' operator S = Σ k≥0 F(k)T k . We obtain asymptotic properties

Pointwise and norm properties of the Brunel operator

  • 2020

Pointwise and norm properties of the Brunel operator. Preprint in preparation

  • 2020

On positive mean-bounded operators

  • Comptes Rendus De L’Académie Des Sciences,
  • 1984

Linear Operators Part I. Interscience

  • 1957

Pointwise and norm properties of the Brunel operator . Preprint in preparation ( 2020 ) . [ BE 84 ] A . Brunel and R . Emilion . On positive mean - bounded operators

  • Comptes Rendus De L ’ Académie Des Sciences
  • 1984