Algebraic extensions of continuous function algebras

Algebraic Extensions of Continuous Function Algebras

Algebraic Extensions of Normed Algebras

Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author's. Acknowledgement: Many thanks to Joel Feinstein for guidance with the literature, useful suggestions and comments on this work.

Some Absolutely Continuous Representations of Function Algebras

In this paper we study some absolutely continuous representations of function algebras, which are weak -spectral in the sense of [5] and [6], for a scalar > 0. Precisely we investigate certain conditions for the existence of a spectral -dilation of such representation. Among others we obtain di¤erent results which generalize the corresponding theorems of D. Gaşpar [3]. Full text

Completely continuous Banach algebras

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

Finite automata and algebraic extensions of function fields

We give an automata-theoretic description of the algebraic closure of the rational function field Fq(t) over a finite field Fq, generalizing a result of Christol. The description takes place within the Hahn-Mal’cev-Neumann field of “generalized power series” over Fq. Our approach includes a characterization of well-ordered sets of rational numbers whose base p expansions are generated by a fini...