• Corpus ID: 224710735

# New Estimates on the bounds of Brunel's operator.

@article{Assani2020NewEO,
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},
year={2020}
}
• Published 17 October 2020
• Mathematics
• 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…

## References

SHOWING 1-10 OF 14 REFERENCES

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
© 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
• Mathematics, Computer Science
• 2015
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].
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

• 2020

• 2020

### On positive mean-bounded operators

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

• 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