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About Several Complex Variables and Banach Algebras
<p>During the past twenty years many connections have been found between the</p><p>theory of analytic functions of one or more complex variables and the study of</p><p>commutative Banach algebras. On the one hand, function theory has been used to</p><p>answer algebraic questions such as the question of the existence of idempotents in</p><p>a Banach algebra. On the other hand, concepts arising from the study of Banach</p><p>algebras such as the maximal ideal space, the ˇ Silov boundary, Gleason parts, etc.</p><p>have led to new questions and to new methods of proof in function theory.</p><p>Roughlyonethirdofthisbookisconcernedwithdevelopingsomeoftheprinci-</p><p>palapplicationsoffunctiontheoryinseveralcomplexvariablestoBanachalgebras.</p><p>Wepresupposenoknowledgeofseveralcomplexvariablesonthepartofthereader</p><p>but develop the necessary material from scratch. The remainder of the book deals</p><p>with problems of uniform approximation on compact subsets of the space of n</p><p>complex variables. For n > 1 no complete theory exists but many important</p><p>particular problems have been solved.</p><p>Throughout, our aim has been to make the exposition elementary and self-</p><p>contained. We have cheerfully sacrificed generality and completeness all along</p><p>the way in order to make it easier to understand the main ideas.</p><p>Relationships between function theory in the complex plane and Banach alge-</p><p>bras are only touched on in this book. This subject matter is thoroughly treated</p><p>in A. Browder’s Introduction to Function Algebras, (W. A. Benjamin, New York,</p><p>1969) and T. W. Gamelin’s Uniform Algebras, (Prentice-Hall, Englewood Cliffs,</p><p>N.J., 1969). A systematic exposition of the subject of uniform algebras including</p><p>many examples is given by E. L. Stout, The Theory of Uniform Algebras, (Bogden</p><p>and Quigley, Inc., 1971).</p><p>The first edition of this book was published in 1971 by Markham Publishing</p><p>Company. The present edition contains the following new Sections: 18. Subman-</p><p>ifolds of High Dimension, 19. Generators, 20. The Fibers Over a Plane Domain,</p><p>21. Examples of Hulls. Also, Section 11 has been revised.</p><p>Exercises of varying degrees of difficulty are included in the text and the reader</p><p>should try to solve as many of these as he can. Solutions to starred exercises are</p><p>given in Section 22.</p>
Detailed Information
| Author: | Herbert Alexander, John Wermer |
|---|---|
| Publication Year: | 1998 |
| ISBN: | 387982531 |
| Pages: | 265 |
| Language: | other |
| File Size: | 3.4485 |
| Format: | |
| Price: | FREE |
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