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A Course in Abstract Analysis
John B. Conway
出版
American Mathematical Soc.
, 2012-10-03
主題
Mathematics / General
ISBN
0821890832
9780821890837
URL
http://books.google.com.hk/books?id=GZQCAQAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
