Banach algebras are Banach spaces equipped with a continuous
multipli- tion. In roughterms, there arethree types ofthem:
algebrasofboundedlinear operators on Banach spaces with composition
and the operator norm, al- bras consisting of bounded continuous
functions on topological spaces with pointwise product and the
uniform norm, and algebrasof integrable functions on locally
compact groups with convolution as multiplication. These all play a
key role in modern analysis. Much of operator theory is best
approached from a Banach algebra point of view and many questions
in complex analysis (such as approximation by polynomials or
rational functions in speci?c - mains) are best understood within
the framework of Banach algebras. Also, the study of a locally
compact Abelian group is closely related to the study 1 of the
group algebra L (G). There exist a rich literature and excellent
texts on each single class of Banach algebras, notably on uniform
algebras and on operator algebras. This work is intended as a
textbook which provides a thorough introduction to the theory of
commutative Banach algebras and stresses the applications to
commutative harmonic analysis while also touching on uniform
algebras. In this sense and purpose the book resembles Larsen's
classical text 75] which shares many themes and has been a valuable
resource. However, for advanced graduate students and researchers I
have covered several topics which have not been published in books
before, including some journal articles.
General
| Imprint: |
Springer-Verlag New York
|
| Country of origin: |
United States |
| Series: |
Graduate Texts in Mathematics, 246 |
| Release date: |
November 2008 |
| First published: |
2009 |
| Authors: |
Eberhard Kaniuth
|
| Dimensions: |
235 x 155 x 20mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
353 |
| Edition: |
1st Edition.
2nd Printing. 2008 |
| ISBN-13: |
978-0-387-72475-1 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
| LSN: |
0-387-72475-3 |
| Barcode: |
9780387724751 |
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