Projectivity of Banach and C*-algebras of continuous fields
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- David Cushing
- Dr Zinaida Lykova
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| Author(s) | | Cushing D, Lykova ZA |
| Publication type | | Article |
| Journal | | The Quarterly Journal of Mathematics |
| Year | | 2013 |
| Volume | | 64 |
| Issue | | 2 |
| Pages | | 341-371 |
| ISSN (print) | | 0033-5606 |
| ISSN (electronic) | | 1464-3847 |
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| Full text for this publication is not currently held within this repository. Alternative links are provided below where available. |
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| We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify projective $C^*$-algebras $\A$ defined by locally trivial continuous fields $\mathcal{U} = \{\Omega,(A_t)_{t \in \Omega},\Theta\}$ such that each $C^*$-algebra $ A_{t}$ has a strictly positive element. For a commutative $C^*$-algebra $\D$ contained in ${\cal B}(H)$, where $H$ is a separable Hilbert space, we show that the condition of left projectivity of $\D$ is equivalent to the existence of a strictly positive element in $\D$ and so to the spectrum of $\D$ being a Lindel$\ddot{\rm o}$f space. |
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| Publisher | | Oxford University Press |
| URL | | http://dx.doi.org/10.1093/qmath/has005 |
| DOI | | 10.1093/qmath/has005 |
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