An Introduction to K-Theory for C*-Algebras (London Mathematical Society Student Texts) [Paperback]

M. Rørdam (Author), F. Larsen (Author), N. Laustsen (Author)

Book Description

Publication Date: July 31, 2000 | ISBN-10: 0521789443 | ISBN-13: 978-0521789448 | Edition: 1

Over the past twenty-five years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The authors cover the basic properties of the functors K and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.

Editorial Reviews

Review

'The textbook is a nice introduction to the subject preparing the ground for the study of more advanced texts.' H. Schröder, Zentralblatt für Mathematik

Book Description

Over the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.

Product Details

• Paperback: 256 pages
• Publisher: Cambridge University Press; 1 edition (July 31, 2000)
• Language: English
• ISBN-10: 0521789443
• ISBN-13: 978-0521789448
• Product Dimensions: 8.9 x 6 x 0.8 inches
• Shipping Weight: 14.9 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,410,802 in Books (See Top 100 in Books)

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5 of 5 people found the following review helpful:

5.0 out of 5 stars Nice place to start..., November 6, 2003

By A Customer

This review is from: An Introduction to K-Theory for C*-Algebras (London Mathematical Society Student Texts) (Paperback)

It's a very clear book with virtually no typos/mistakes and lots of nice exercises (if you are willing to do them - highly recommended). Really an introductory text, so you might need to consult the more advanced books of Wegge-Olsen, Blackadar after this one for more information on the subject. Nice place to start, especially if it is for self-study.

2 of 2 people found the following review helpful:

5.0 out of 5 stars One of the best two introductory titles along with Wegge-Olsen, November 23, 2008

By 

Farshid Arjomandi (California, USA) - See all my reviews
(REAL NAME)   

This review is from: An Introduction to K-Theory for C*-Algebras (London Mathematical Society Student Texts) (Paperback)

K-theory is a branch of algebraic topology originally concerned with the study of vector bundles by algebraic means. The first notions of the theory were put forward by Alexander Groethendieck in his work on the Riemann-Roch theorem in algebraic geometry, and early in the 60's it was developed into a branch of algebraic topology by M. Atiyah and F. Hirzebruch. From the analysis perspective, K-theory has a very natural link with the theory of Fredholm operators on a compact manifold and hence to the famous Atiyah-Singer index theorem. In the recent decades the theory has revolutionized the study of the structure theory of certain operator algebras. The procedure involves defining a collection of functors {K_n} from the category of C*-algebras to the category of abelian groups, satisfying the Eilenberg-Steenrod axioms for a homology theory. Bott periodicity as a handy feature then implies that there are only two such functors. In this nice text, the readers will find the needed material on C*-algebras, as well as an exposition of the K_0 and K_1 functors leading to the exploration of the Bott periodicity theorem and the six term exact sequence. As a graduate student a few years ago I attempted giving a seminar talk on this topic but was overwhelmed with the task of fitting the needed discussion into a 60-minute time span, specially in a way that the majority of the attendees could follow on. The exposition is indeed heavily algebraic in nature and hence anyone attempting to read and digest it properly will have to possess a strong background in the ideas and methods of basic algebraic topology.