相关论文: New Estimates on the bounds of Brunel's operator

Following Berm\'udez et al. (ArXiv: 1706.03638v1), we study the rate of growth of the norms of the powers of a linear operator, under various resolvent conditions or Ces\`aro boundedness assumptions. We show that $T$ is power-bounded if…

A Ritt operator T : X --> X on Banach space is a power bounded operator such that the sequence of all n(T^{n} -T^{n-1}) is bounded. When X=Lp for some 1<p<\infty, we study the validity of square functions estimates Norm{(\sum_k k |T^{k}(x)…

We consider whether L = limsup_{n to infty} n ||T^{n+1}-T^n|| < infty implies that the operator T is power bounded. We show that this is so if L<1/e, but it does not necessarily hold if L=1/e. As part of our methods, we improve a result of…

Necessary and sufficient conditions are presented for the Abel averages of discrete and strongly continuous semigroups, $T^k$ and $T_t$, to be power convergent in the operator norm in a complex Banach space. These results cover also the…

Let $T$ be a bounded operator. We say $T$ is a Ritt operator if $\sup_n n\lVert T^n-T^{n+1}\rVert<\infty$. It is know that when $T$ is a positive contraction and a Ritt operator in $L^p$, $1<p<\infty$, then for any integer $m\ge 1$, the…

Let $T$ be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages $N^{-1}\sum_{n=1}^N T^{a_n}$ converge in the strong operator topology for a wide range of sequences $(a_n)$,…

Let $\mathcal D$ be a Schauder decomposition on some Banach space $X$. We prove that if $\mathcal D$ is not $R$-Schauder, then there exists a Ritt operator $T\in B(X)$ which is a multiplier with respect to $\mathcal D$, such that the set…

Let $G$ be a locally compact abelian group, let $\nu$ be a regular probability measure on $G$, let $X$ be a Banach space, let $\pi\colon G\to B(X)$ be a bounded strongly continuous representation. Consider the average (or subordinated)…

Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…

We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In…

Let $c=(C_n)_{n\ge 0}$ be the Catalan sequence and $T$ a linear and bounded operator on a Banach space $X$ such $4T$ is a power-bounded operator. The Catalan generating function is defined by the following Taylor series, $$…

Let $T\colon X\to X$ be a bounded operator on Banach space, whose spectrum $\sigma(T)$ is included in the closed unit disc $\overline{\mathbb D}$. Assume that the peripheral spectrum $\sigma(T)\cap{\mathbb T}$ is finite and that $T$…

We introduce the class of $\alpha$-firmly nonexpansive and quasi $\alpha$-firmly nonexpansive operators on $r$-uniformly convex Banach spaces. This extends the existing notion from Hilbert spaces, where $\alpha$-firmly nonexpansive…

Let $T$ be a power-bounded operator on a Banach space $X$, $\mathcal{A}$ be a Banach algebra of bounded holomorphic functions on the unit disc $\mathbb{D}$, and assume that there is a bounded functional calculus for the operator $T$, so…

In this paper, we investigate power-bounded operators, including surjective isometries, on Banach spaces. Koehler and Rosenthal asserted that an isolated point in the spectrum of a surjective isometry on a Banach space lies in the point…

Let $T$ be a bounded linear operator on a Hilbert space $H$ such that \[ \alpha[T^*,T]:=\sum_{n=0}^\infty \alpha_n T^{*n}T^n\ge 0. \] where $\alpha(t)=\sum_{n=0}^\infty \alpha_n t^n$ is a suitable analytic function in the unit disc…

Given Hilbert space operators $P,T\in B(\H), P\geq 0$ invertible, $T$ is $(m,P)-$ expansive (resp., $(m,P)-$ isometric) for some positive integer $m$ if…

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 $\left\{ A^{n}TB^{n}\right\} $ and…

For $\xi \in \big(0, {1/2} \big)$, we denote by $E_{\xi}$ the perfect symmetric set associated to $\xi$, that is $$ E_{\xi} = \Big\{\exp \big(2i \pi (1-\xi) \dsp \sum_{n = 1}^{+\infty} \epsilon_{n} \xi^{n-1} \big) : \epsilon_{n} = 0…

$T$ is a Ritt operator in $L^p$ if $\sup_n n\|T^n-T^{n+1}\|<\infty$. From \cite{LeMX-Vq}, if $T$ is a positive contraction and a Ritt operator in $L^p$, $1<p<\infty$, the square function $\left( \sum_n n^{2m+1} |T^n(I-T)^{m+1}f|^2…