论文标题
迭代的对数Lipschitz的乘法操作员
Multiplication operators on the iterated logarithmic Lipschitz spaces of a tree
论文作者
论文摘要
我们介绍了一类迭代的对数Lipschitz空间$ \ MATHCAL {l}^{（k）} $，$ k \ in \ Mathbb {n} $，在无限树上，在操作员理论的背景下自然出现。我们表征了乘法运算符的有限性和紧凑性，上面是$ \ Mathcal {l}^{（k）} $，并提供有关其运算符规范及其基本规范的估计值。此外，我们确定频谱，表征下面有界的乘法运算符，并证明在此类空间上没有非平凡的等距乘法运算符，也没有等距为零的零除数。
We introduce a class of iterated logarithmic Lipschitz spaces $\mathcal{L}^{(k)}$, $k\in\mathbb{N}$, on an infinite tree which arise naturally in the context of operator theory. We characterize boundedness and compactness of the multiplication operators on $\mathcal{L}^{(k)}$ and provide estimates on their operator norm and their essential norm. In addition, we determine the spectrum, characterize the multiplication operators that are bounded below, and prove that on such spaces there are no nontrivial isometric multiplication operators and no isometric zero divisors.
