In this paper, we prove the following theorem: Let {T (t) : t ≥ 0} be a one-parameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T (t) is denoted by F (

Derndinger [Der80] and Krupa [Kru90] defined the F–product of a (strongly continuous one–parameter) semigroup (of linear operators) and presented some applications (e.g. to spectral theory of positive operators, cf. [EN00]). Wolff (in [Wol84] and [Wol00]) investigated some kind of nonstandard analogon and applied it to spectral theory of group representations. The question arises in which way t...

A basic result in semigroup theory states that every C0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e t n P ) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introd...

This note shows how iteration of the standard process of adjoining identities and zeros to semigroups gives rise naturally to the lexicographical ordering on the additive semigroups of n-tuples of nonnegative integers and n-tuples of integers. 1. Semigroups with identities and zeros A binary operation ∗ on a set S is associative if (a ∗ b) ∗ c = a ∗ (b ∗ c) for all a, b, c ∈ S. A semigroup is a...

We analyse the average case complexity of evaluating all preexes of an input vector over a given semigroup. As computational model circuits over the semigroup are used and a complexity measure for the average delay of such circuits, called time, is introduced. Based on this notion, we then deene the average case complexity of a computational problem for arbitrary input distributions. For highly...

We consider certain properties of the semigroup S defined by the presentation S = 〈a, b : a n−1 = 1, b = a n−2 , ba = ab n−1−1〉, (n ≥ 3).

Abstract. In this article we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to “largeness”. The first property is ID and the other property is maximal commutativity (MC). A semigroup has the ID property if the only infinite invariant closed set (with respect to the ...

Considered is the multiplicative semigroup of ratios of products of principal minors bounded over all positive definite matrices. A long history of literature identifies various elements of this semigroup, all of which lie in a subsemigroup generated by Hadamard-Fischer inequalities. Via cone-theoretic techniques and the patterns of nullity among positive semidefinite matrices, a semigroup cont...