Books by "Harold G. Dales"
3 books found
Banach Algebras on Semigroups and on Their Compactifications
by Harold G. Dales, Anthony To-Ming Lau, Dona Strauss
2010 · American Mathematical Soc.
"Volume 205, number 966 (end of volume)."
The Second Duals of Beurling Algebras
by Harold G. Dales, Anthony To-Ming Lau
2005 · American Mathematical Soc.
Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.
Super-real fields are a class of large totally ordered fields. These fields are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are of interest in their own right and have many surprising applications, both in analysis and logic. The authors introduce some exciting new fields, including a natural generalization of the real line R, and resolve a number of open problems. The book is intended to be accessible to analysts and logicians. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kaplansky's embedding theorems , the authors establish important new results in Banach algebra theory, non-standard analysis, an model theory.