We initiate the study of the forward and backward shifts on the Lipschitz space of an undirected tree, $$\mathcal {L}$$ L , and on the little Lipschitz space of an undirected tree, $$\mathcal {L}_0$$ L 0 . We determine that the forward shift is bounded both on $$\mathcal {L}$$ L and on $$\mathcal {L}_0$$ L 0 and, when the tree is leafless, it is an isometry; we also calculate its spectrum. For the backward shift, we determine when it is bounded on $$\mathcal {L}$$ L and on $$\mathcal {L}_0$$ L 0 , we find the norm when the tree is homogeneous, we calculate the spectrum for the case when the tree is homogeneous, and we determine, for a general tree, when it is hypercyclic.

中文翻译：

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一棵树的 Lipschitz 空间的前后移动

我们开始研究无向树的 Lipschitz 空间 $$\mathcal {L}$$ L 和无向树的小 Lipschitz 空间 $$\mathcal {L}_0$ 上的向前和向后移动$L 0 。我们确定前移在 $$\mathcal {L}$$ L 和 $$\mathcal {L}_0$$ L 0 上都有界，并且当树无叶时，它是等距的；我们还计算了它的频谱。对于后移，我们确定当它在 $$\mathcal {L}$$ L 和 $$\mathcal {L}_0$$ L 0 上有界时，我们找到树齐次时的范数，我们计算当树是齐次的情况下的频谱，我们确定，对于一般树，当它是超循环时。