Lectures on Amenability / Edition 1

Paperback (Print)
Buy New
Buy New from BN.com
$63.96
Used and New from Other Sellers
Used and New from Other Sellers
from $59.72
Usually ships in 1-2 business days
(Save 25%)
Other sellers (Paperback)
  • All (5) from $59.72   
  • New (4) from $59.72   
  • Used (1) from $131.99   

Overview

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra Lsub1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.

Read More Show Less

Product Details

  • ISBN-13: 9783540428527
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 1/10/2002
  • Series: Lecture Notes in Mathematics Series , #1774
  • Edition description: 2002
  • Edition number: 1
  • Pages: 296
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.66 (d)

Table of Contents

0 Paradoxical decompositions
0.1 The Banach-Tarski paradox
0.2 Tarski's theorem
0.3 Notes and comments

1 Amenable, locally comact groups
1.1 Invariant means on locally compact groups
1.2 Hereditary properties
1.3 Day's fixed point theorem
1.4 Representations on Hilbert space
1.5 Notes and comments

2 Amenable Banach algebras
2.1 Johnson's theorem
2.2 Virtual and approximate diagonals
2.3 Hereditary properties
2.4 Hochschild cohomology
2.5 Notes and comments

3 Exemples of amenable Banach algebras
3.1 Banach algebras of compact operators
3.2 A commutative, radical, amenable Banach algebra
3.3 Notes and comments

4 Amenability-like properties
4.1 Super-amenability
4.2 Weak amenability
4.3 Biprojectivity and biflatness
4.4 Connes-amenability
4.5 Notes and comments

5 Banach homology
5.1 Projectivity
5.2 Resolutions and Ext-groups
5.4 Flatness and injectivity
5.4 Notes and Comments

6 C* and W*-algebras
6.1 Amenable W*-algebras
6.2 Injective W*-algebras
6.3 Tensor products of C*- and W*-algebras
6.4 Semidiscrete W*-algebras
6.5 Normal, virtual diagonals
6.6 Notes and comments

7.1 Bounded approximate identities for Fourier algebras
7.2 (Non-)amenability of Fourier
7.3 Operator amenable operator Banach algebras
7.4 Operator amenability of Fourier algebras
7.5 Operator amenability of C*-algebras
7.6 Notes and comments

8 Geometry of spaces of homomorphisms
8.1 Infinite-dimensional differential geometry
8.2 Spaces of homomorphisms
8.3 Notes and Comments

Open problems

A Abstract harmonic analysis
A.1 Convolution of measures and functions
A.2 Invariant subspaces of L(infinity symbol)(G)
A.3 Regular representations on Lp(G)
A.4 Notes and comments

B.1 The algebraic tensor products
B.2 Banach space tensor products
B.2.1 The injective tensor product
B.2.2 The projective tensor product
B.3 The Hilbert space tensor product
B.4 Notes and comments

C Banach space properties
C.1 Approximation properties
C.2 The Radon-Nikokym property
C.3 Local theory of Banach spaces
C.4 Notes and comments

D Operator spaces
D.1 Abstract and concrete operator spaces
D.2 Completely bounded maps
D.3 Tensor products of operator spaces
D.4 Operator Banach algebras
D.5 Notes and comments
List of symbols
References
Index

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)