A Course in Abstract Analysis (Graduate Studies in Mathematics, Vol. 141) - Hardcover

John B. Conway

Hardcover

ISBN 10: 0821890832 ISBN 13: 9780821890837

Publisher: American Mathematical Society, 2012

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2012
• Language: English
• ISBN 10: 0821890832
• ISBN 13: 9780821890837
• Binding: Hardcover
• Edition number: 1
• Number of pages: 367