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Banach Algebras on Semigroups and on Their Compactifications

H. G. Dales University of Leeds, Leeds, England
A. T.-M. Lau University of Alberta, Edmonton, AB, Canada
D. Strauss University of Leeds, Leeds, England
Available Formats:
Electronic ISBN: 978-1-4704-0580-9
Product Code: MEMO/205/966.E
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $46.80 Click above image for expanded view Banach Algebras on Semigroups and on Their Compactifications H. G. Dales University of Leeds, Leeds, England A. T.-M. Lau University of Alberta, Edmonton, AB, Canada D. Strauss University of Leeds, Leeds, England Available Formats:  Electronic ISBN: 978-1-4704-0580-9 Product Code: MEMO/205/966.E  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$46.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 2052010; 165 pp
MSC: Primary 43; Secondary 46;

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.

• Chapters
• 1. Introduction
• 2. Banach algebras and their second duals
• 3. Semigroups
• 4. Semigroup algebras
• 5. Stone–Čech compactifications
• 6. The semigroup $(\beta S, \Box )$
• 7. Second duals of semigroup algebras
• 8. Related spaces and compactifications
• 9. Amenability for semigroups
• 10. Amenability of semigroup algebras
• 11. Amenability and weak amenability for certain Banach algebras
• 12. Topological centres
• 13. Open problems
• Requests

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Volume: 2052010; 165 pp
MSC: Primary 43; Secondary 46;

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.

• Chapters
• 1. Introduction
• 2. Banach algebras and their second duals
• 3. Semigroups
• 4. Semigroup algebras
• 5. Stone–Čech compactifications
• 6. The semigroup $(\beta S, \Box )$
• 7. Second duals of semigroup algebras
• 8. Related spaces and compactifications
• 9. Amenability for semigroups
• 10. Amenability of semigroup algebras
• 11. Amenability and weak amenability for certain Banach algebras
• 12. Topological centres
• 13. Open problems
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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