Product Description: Let $S$ be a (discrete) semigroup, and let $\ell^{\,1}(S)$ be the Banach algebra which is the semigroup algebra of $S$. The authors study the structure of this Banach algebra and of its second dual. The authors determine exactly when $\ell^{\,1}(S)$ is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are 'forbidden values' for this constant...read more

Product Description: 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 $A""$...read more

Product Description: Based on lectures given at an instructional course, this volume enables readers with a basic knowledge of functional analysis to access key research in the field. The authors survey several areas of current interest, making this volume ideal preparatory reading for students embarking on graduate work as well as for mathematicians working in related areas...read more (view table of contents, read Amazon.com's description)

Product Description: This volume expounds the general theory of Banach algebras and shows how their topology is often determined by their algebraic structures. It synthesizes work in this area from the past 20 years, including many new and unpublished results, and probes the questions of when homomorphisms and derivations from Banach algebras are automatically continuous and seeks canonical forms for these maps...read more (view table of contents, read Amazon.com's description)

Product Description: In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\0\rightarrow I\rightarrow\mathfrak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\mathfrak A$ is a Banach algebra and $I$ is a closed ideal in $\mathfrak A$...read more

Product Description: The nature of truth in mathematics has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth century and in particular the work by Gödel and the development of the notion of independence in mathematics have led to new and complex views on this question...read more (view table of contents, read Amazon.com's description)

Product Description: This book is of interest for students of mathematics or of neighboring subjects like physics, engineering, computer science, and also for people who have at least school level mathematics and have kept some interest in it. Also good for younger readers just reaching their final school year of mathematics...read more

Product Description: Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC...read more