The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. <P>This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty years has been based on a careful study of these special classes. While there are many books on C*-algebras and operator algebras available, this is the first one to attempt to explain the real examples that researchers use to test their hypotheses. Topics include AF algebras, Bunce-Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, group C*-algebras, discrete crossed products, abelian C*-algebras (spectral theory and approximate unitary equivalence) and extensions. It also introduces many modern concepts and results in the subject such as real rank zero algebras, topological stable rank, quasidiagonality, and various new constructions. <P>These notes were compiled during the author's participation in the special year on C*-algebras at The Fields Institute for Research in Mathematical Sciences during the 1994-1995 academic year. The field of C*-algebras touches upon many other areas of mathematics such as group representations, dynamical systems, physics, $K$-theory, and topology.
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取材相當的新穎，也有一定深度，為什麼隻給四星呢？主要是敘述方式不和胃口，充滿著冗長的初等技術討論，像最後的Busby map竟然連名稱都不給一個，隻讓讀者看到一堆亂糟糟的映射箭頭在復閤，建議讀者像我這樣用跳躍式的方式閱讀自己感興趣的部分。
评分取材相當的新穎，也有一定深度，為什麼隻給四星呢？主要是敘述方式不和胃口，充滿著冗長的初等技術討論，像最後的Busby map竟然連名稱都不給一個，隻讓讀者看到一堆亂糟糟的映射箭頭在復閤，建議讀者像我這樣用跳躍式的方式閱讀自己感興趣的部分。
评分用大量的例子來討論c*代數，前兩章給齣算子代數的基本理論，三四兩章給齣AF代數的分類方法，並解釋用基本的K理論來分類AF代數。五六七八章給齣重要的C*代數的例子及其結構的研究方法，最後一章是精髓。不過前兩章內容過於簡略，導緻初學這本書十分睏難。還是先看conway的兩本書吧。
评分用大量的例子來討論c*代數，前兩章給齣算子代數的基本理論，三四兩章給齣AF代數的分類方法，並解釋用基本的K理論來分類AF代數。五六七八章給齣重要的C*代數的例子及其結構的研究方法，最後一章是精髓。不過前兩章內容過於簡略，導緻初學這本書十分睏難。還是先看conway的兩本書吧。
评分取材相當的新穎，也有一定深度，為什麼隻給四星呢？主要是敘述方式不和胃口，充滿著冗長的初等技術討論，像最後的Busby map竟然連名稱都不給一個，隻讓讀者看到一堆亂糟糟的映射箭頭在復閤，建議讀者像我這樣用跳躍式的方式閱讀自己感興趣的部分。
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