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Item Details
| Title:
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ALGEBRAIC AND STRONG SPLITTINGS OF EXTENSIONS OF BANACH ALGEBRAS
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| By: |
W.G. Bade, etc., H. G. Dales |
| Format: |
Paperback |
| List price:
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£46.95 |
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| ISBN 10: |
0821810588 |
| ISBN 13: |
9780821810583 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 1999 |
| Series: |
Memoirs of the American Mathematical Society No. 656 |
| Pages: |
113 |
| Description: |
Addresses the following: Let $A$ be a Banach algebra, and let $\sum\:\0\rightarrow I\rightarrow\mathfrak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\mathfrak A$ is a Banach algebra and $I$ is a closed ideal in $\mathfrak A$. |
| Synopsis: |
In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\0\rightarrow I\rightarrow\mathfrak A\overset\pi\to\longrightarrow A\rightarrow 0$ 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) $\theta\: A\rightarrow\mathfrak A$ such that $\pi\circ\theta$ 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) Wedderbum 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 $A$. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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