This text provides an up-to-date account of Banach and locally convex algebras with a particular emphasis on general theory, representations, and homology. In his descriptions and examples of general theory, the author remains aware of traditional trends in the field analysis while breaking from convention in his approach to "the algebra of analysis" through homological algebra. Such an approach allows Helemskii to consider topics not covered at this level in any other book, including complemented and uncomplemented ideals, projective and weak tensor products of banach algebras, Taylor's...

'Et moi .... si j'avait su comment en revenir. One service mathematics has rendered the human race. It has put common sense back je n'y serais point aUe.' it belongs. on the topmost shelf next Jules Verne where to the dusty canister labelled 'discarded non. The series is divergent: therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

Based on courses taught by the author at Moscow State University, this book features such topics as the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. It contains many examples il