C*-Algebras by Example pdf epub mobi txt 電子書下載在線閱讀 2026

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出版者:American Mathematical Society

作者:Kenneth R. Davidson

出品人:

頁數:309

译者:

出版時間:1996-7-30

價格:GBP 65.95

裝幀:Hardcover

isbn號碼:9780821805992

叢書系列:

圖書標籤:

數學
C*-algebras
Operator algebras
Functional analysis
Noncommutative geometry
Mathematical physics
Representation theory
K-theory
Spectral theory
Banach algebras
Operator systems

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具體描述

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.

這本書《C-Algebras by Example》旨在通過豐富且易懂的方式，為讀者提供對C-代數這一重要的數學工具的全麵介紹。書中內容緊密圍繞實際例子展開，幫助學生和愛好者深入理解抽象概念，並將其具體化到具體應用場景中。每一章節都以清晰邏輯的結構設計，確保讀者能夠一步步掌握所學知識。書中首先對C-代數的基本定義進行瞭詳細解析，這是理解後續內容的基礎。在這一部分，作者引入瞭一些常見的例子，如緊算子、環狀群和連續函數空間，通過具體案例讓讀者直觀感受這些概念的構成。通過這些實例，讀者能夠更容易地將理論與實際聯係起來，從而加深理解。接下來，書籍係統地展開瞭C-代數的性質和結構，特彆是其在分析空間中的錶現。這部分內容深入探討瞭狀態、連續算子以及拓撲性質等重要方麵，每個主題都配有相應的例子，使得難度適中且易於學習。讀者不僅能理解理論內涵，還能通過具體示例加深記憶。書中的另一大特色是其強調實踐應用，尤其是在數學物理和量子力學領域的作用。通過詳細描述這些應用場景，書籍幫助讀者瞭解C-代數在真實研究中的重要地位。這不僅拓寬瞭知識麵，還激發瞭對該主題的興趣。此外，書中還特彆注重教學技巧的設計，采用問題引導、思考練習和總結環節，使每個章節都成為讀者思考的起點。這種積極參與式學習方式，有助於提升理解深度，並培養獨立思考能力。作者在整個書中運用瞭多樣化的教學方法，從定義講解到實際應用，再到深入分析，每一步都經過精心設計，確保內容既嚴謹又易懂。書中對不同層次讀者的需求均有充分考慮，適閤從初學者到進階學習者使用。通過係統性和詳細的介紹，這本書不僅幫助讀者掌握C-代數的基本知識，還為進一步深入研究提供瞭堅實的基礎。它是一本兼具理論與實踐價值的高質量資源，旨在培養懂事解題的數學思維能力。總體來說，這本書以清晰、詳盡和豐富的內容，為讀者帶來深入而全麵的學習體驗。無論是學生還是研究者，都能從中獲得有價值的參考。這種對細節的關注，使每一章都成為學習過程中的重要節點，確保知識傳遞的高效性與準確性。