Algebraic and Strong Splittings of Extensions of Banach Algebras(Memoirs of the American Mathematical Society)

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作      者
出版时间
1999年01月30日
装      帧
平装
ISBN
9780821810583
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页      码
113
语      种
英文
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In this volume, the authors address the following: Let (A) be a Banach algebra, and let (sum: 0rightarrow Irightarrowmathfrak Aoversetpitolongrightarrow Arightarrow 0) be an extension of (A), where (mathfrak A) is a Banach algebra and (I) is a closed ideal in (mathfrak A). The extension splits algebraically (respectively, splits strongly) if there is a homomorphism (respectively, continuous homomorphism) (theta: Arightarrowmathfrak A) such that (picirctheta) is the identity on (A). Consider first for which Banach algebras (A) it is true that every extension of (A) in a particular class of extensions splits, either algebraically or strongly, and second for which Banach algebras it is true that every extension of (A) in a particular class which splits algebraically also splits strongly. These questions are closely related to the question when the algebra (mathfrak A) has a (strong) Wedderburn decomposition. The main technique for resolving these questions involves the Banach cohomology group (mathcal H^2(A,E)) for a Banach (A)-bimodule (E), and related cohomology groups. Later chapters are particularly concerned with the case where the ideal (I) is finite-dimensional. Results are obtained for many of the standard Banach algebras (A).
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