论文标题
Fell Bundles的傅立叶和傅立叶 - 斯泰尔杰斯代数
Fourier and Fourier-Stieltjes algebra of Fell bundles over discrete groups
论文作者
论文摘要
对于倒束$ \ nathcal {b} = \ left \ {b_ {b_ {s} \ right \} _ {s \ in g} $在一个离散组$ g $上，我们使用$ \ nathcal {b} $的表示理论来构建fourier and fourier-stieltjes $ a（ $ b（\ MATHCAL {B}）$ \ MATHCAL B $。当$ \ Mathcal b $饱和时，我们显示$ b（\ Mathcal {b}）$在规范上是同构的，对于横截面$ c^{*} $ - algebra $ c^{*}（\ Mathcal {b}）$ $ \ Mathcal {b} $ {当纤维上有一个兼容的共同质子家族时，我们表明$ b（\ mathcal {b}）$和$ a（\ Mathcal {b}）$是Banach代数。这特别是如果fiber $ b_e $处于身份是hopf $ c^*$ - 代数或$ \ mathcal {b} $是$ c^*$ - 动力系统的fly束。当$ a（\ Mathcal {b}）$是具有有界近似身份的Banach代数时，我们表明$ b（\ Mathcal {b}）$是$ a（\ Mathcal {b}）$的乘数代数。我们通过证明$ g $的固定性意味着$ a（\ Mathcal {b}）$的有限近似身份来证明瘦素类型定理，这是来自$ c^*$ - 动力系统$（a，g，γ）$的捆绑包。相反的问题是一个开放问题。
For a Fell bundle $\mathcal{B}=\left\{B_{s}\right\}_{s \in G}$ over a discrete group $G$, we use representations theory of $\mathcal{B}$ to construct the Fourier and Fourier-Stieltjes spaces $A(\mathcal{B})$ and $B(\mathcal{B})$ of $\mathcal B$. When $\mathcal B$ is saturated we show $B(\mathcal{B})$ is canonically isomorphic to the dual space of the cross sectional $C^{*}$-algebra $C^{*}(\mathcal{B})$ of $\mathcal{B}$. When there is a compatible family of co-multiplications on the fibers we show that $B(\mathcal{B})$ and $A(\mathcal{B})$ are Banach algebras. This holds in particular if either the fiber $B_e$ at identity is a Hopf $C^*$-algebra or $\mathcal{B}$ is the Fell bundle of a $C^*$-dynamical system. When $A(\mathcal{B})$ is a Banach algebra with bounded approximate identity, we show that $B(\mathcal{B})$ is the multiplier algebra of $A(\mathcal{B})$. We prove a Leptin type theorem by showing that amenability of $G$ implies the existence of bounded approximate identity for $A(\mathcal{B})$ for bundles coming from a $C^*$-dynamical system $(A,G,γ)$. The converse is left as an open problem.
