A reference textbook that summarizes the "algebra of analysis" that includes some mention of the contemporary trends in the development of history. This text provides an up-to-date account of Banach and locally convex algebras with emphasis on general theory, representations and homology. In its description of general theory and in the examples it considers it is faithful to earlier traditions in the subject but differs from those books in being based on an
approach through homological algebra. This approach leads Helemskii to consider topics not covered at this level in any other book. These topics include: complemented and uncomplemented ideal; projective and weak tensor products of banach algebras; Taylors multivariable holomorphic functional calculus; the
Wedderburn decomposition of Banach algevras; a whole chapter on the homology of Banach algebras.
'This text provides an up-to-date account of Banach and locally convex algebras.'
L'Enseignement Mathématique, 3-4 1993
`a useful and enjoyable book'
Bulletin of the London Mathematical Society, 27, 1995
`Besides the mathematical quality of the book, the reviewer wants also to remark here the charming style of the presentation'
C. Badea, Zbl. Math, 785
Chapter 0. Foundations
Chapter I. Initial concepts and first results
Chapter II. Around the spectrum
Chapter III. Basic stock of examples
Chapter IV. Commutative and star Banach algebras
Chapter V. Polynormed algebras that are near to Banach algebras
Chapter VI. Modules, they are also representations
Chapter VII. Problems leading to homology and the elements of homology theory
Index of notation
Series: Oxford Science Publications
Number Of Pages: 464
Published: 20th May 1993
Country of Publication: GB
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.9