General Theory of Banach Algebras (Repost)
C. E. Rickart, "General Theory of Banach Algebras"
1974 | pages: 407 | ISBN: 0882750917 | PDF | 6 mb
1974 | pages: 407 | ISBN: 0882750917 | PDF | 6 mb
A Banach algebra is a linear associative algebra which, as a vector space, is a Banach space with norm satisfying the multiplicative inequality || xy || =< || x || y ||. Many of the Banach spaces which occur in analysis are at the same time Banach algebras under a multiplication operation which is itself important for the analysis. A good example is the space of absolutely integrable functions on the infinite real line under convolution as multiplication. In spite of the fact that examples from analysis have always provided the main impetus to the study of Banach spaces, a comparable interest in Banach algebras was rather late in coming. Some of the reason lies no doubt in the absence of appropriate algebraic tools, since a large part of the earlier work in algebra was based on finiteness conditions which rule out the most interesting examples from analysis.
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