Multipliers of locally compact quantum groups via Hilbert C *-modules
Multipliers of locally compact quantum groups via Hilbert C *-modules
复制标题
通过 Hilbert C * 模的局部紧量子群乘子
DOI：
10.1112/jlms/jdr013
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Daws M
中科院分区：
文献类型：
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作者：
Daws M
Gilbert的结果表明，傅里叶代数aa (G)的每一个完全有界乘子都是由一对有界连续映射α， β:G→K产生的，其中K是Hilbert空间，f(s‐1t) = (β(t) | α (s))，对于所有，tϵG。我们用作用于某些HilbertC*‐模之间的可伴算子来重新表述这一概念，并证明了一个类似的构造适用于局部紧量子群的完全有界左乘子。我们找到了各种方法来处理右乘数：其中一种方法涉及到观察相反的量子群，这就证明了（无界）对跖点作用于完全有界乘数的空间，以一种与我们的表示结果自然交互的方式。普遍量子群的对偶（在Kustermans意义上）可以用完全有界乘子的子代数来标识，并且我们展示了它如何适合我们的框架。最后，这激发了一种处理双边乘数的方法。
A result of Gilbert shows that every completely bounded multiplierfof the Fourier algebraA(G) arises from a pair of bounded continuous maps α, β :G→K, whereKis a Hilbert space, andf(s‐1t) = (β(t) | α (s)) for alls, tϵG. We recast this in terms of adjointable operators acting between certain HilbertC*‐modules, and show that an analogous construction works for completely bounded left multipliers of a locally compact quantum group. We find various ways to deal with right multipliers: one of these involves looking at the opposite quantum group, and this leads to a proof that the (unbounded) antipode acts on the space of completely bounded multipliers in a way that interacts naturally with our representation result. The dual of the universal quantum group (in the sense of Kustermans) can be identified with a subalgebra of the completely bounded multipliers, and we show how this fits into our framework. Finally, this motivates a certain way of dealing with two‐sided multipliers.