A Note on Infinitesimal Generators of Semigroups on H2/φH2

Infinitesimal Generators Associated with Semigroups of Linear Fractional Maps

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C, n ≥ 1. For the case n = 1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional...

On Landau’s type inequalities for infinitesimal generators∗

We consider Landau’s type inequalities of the form ‖Aku‖n ≤ Cn,k‖u‖n−k‖Anu‖k, u ∈ D(A), 0 < k < n, where A is the infinitesimal generator of either a strongly continuous semigroup or a strongly continuous cosine function of linear contractions on a Banach space X. The constants Cn,k are computed for n ≤ 6.

A Note on Extending Semicharacters on Semigroups

The purpose of this note is to give a necessary and sufficient condition for a semicharacter on a subsemigroup of a commutative semigroup G to be extendable to a semicharacter on G. A bounded complex function x on a semigroup G is called a semicharacter of G if x(x)9^0 for some xEG and x(xy) = x(%)x(y) ior all x, yEG. Semicharacters were introduced by Hewitt and Zuckerman [l] and in a slightly ...

A Note on Representations of Inverse Semigroups

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...

A Note on Amalgams of Inverse Semigroups