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Banach Algebras on Semigroups and on Their Compactifications
TLDR
In this article, the authors studied the structure of the second dual of the semigroup algebra and its amenability constant, showing that there are 'forbidden values' for this constant.Abstract:
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. Table of Contents: Introduction; Banach algebras and their second duals; Semigroups; Semigroup algebras; Stone-?ech compactifications; The semigroup $(\beta S, \Box)$; Second duals of semigroup algebras; Related spaces and compactifications; Amenability for semigroups; Amenability of semigroup algebras; Amenability and weak amenability for certain Banach algebras; Topological centres; Open problems; Bibliography; Index of terms; Index of symbols. (MEMO/205/966)read more
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Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
TL;DR: In this article, a theory of Hardy and BMO spaces associated to a metric space with doubling measure is presented, including an atomic decomposition, square function characterization, and duality of Hardy spaces.
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Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
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On character amenable Banach algebras
TL;DR: Character amenability is a cohomological property weaker than the classical amenability introduced by B.E. Johnson as discussed by the authors, and it is characterized in terms of bounded approximate identities and certain topologically invariant elements of the second dual.
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Biflatness of semigroup algebras
TL;DR: In this paper, the authors studied the biflatness of the convolution algebra l 1(S) for a semigroup S such that the canonical partial ordering on the idempotents must be uniformly locally finite.
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Second duals of measure algebras
TL;DR: In this article, the Arens products on the second dual A′′ of A arising from left and right translations by elements of A are defined, and they are referred to as ♦ and ♦, respectively.
References
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Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
Abstract Harmonic Analysis
Edwin Hewitt,Kenneth A. Ross +1 more
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and prices and other details are subject to change without notice. All errors and omissions excepted.
Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
Journal ArticleDOI
Rings of Continuous Functions.
Book
Fundamentals of semigroup theory
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.