7 papers
Do some nontrivial closed z-invariant subspaces have the division property ?
Jean Esterle
We consider Banach spaces E of functions holomorphic on the open unit disc D such that the unilateral shift S and the backward shift T are bounded on E. Assuming that the spectra o…
A holomorphic functional calculus for finite families of commuting semigroups
Jean Esterle
Let A be a commutative Banach algebra such that uA = {0} for u A \ {0} which possesses dense principal ideals. The purpose of the paper is to give a general framework to defi…
On the generation of Arveson weakly continuous semigroups
Jean Esterle
We consider here one-parameter semigroups of bounded operators on a Banach space which are weakly continuous in the sense of Arveson. For such a semigrou…
Estimates near the origin for functional calculus on analytic semigroups
I. Chalendar, J. Esterle, J. R. Partington
This paper provides sharp lower estimates near the origin for the functional calculus of a generator of an operator semigroup defined on a sector; here is given as…
A short proof of the zero-two law for cosine functions
Jean Esterle
Let $(C(t))\in\mathbb{R}}$ be a cosine function in a unital Banach algebra. We give a simple proof of the fact that if lim sup$\_{t\to 0}\vert C(t)-1\_A\vert\textless{}2,$ then $li…
A zero-sqrt(5)/ 2 law for cosine families
Jean Esterle
Let and let be the largest constant such that $sup\vert cos(na)-cos(nb)\vert \textless{} k(a)$ for implies that We show that if a…