有向树上的加权移位。它们的乘子代数、自反性和分解
Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions
摘要：
研究了有向树上的有界加权移位。我们证明了根有向树上与单射加权移位相关的乘法算子集与加权移位多项式集的WOT/SOT闭包一致。从这个事实，我们推出的自反性的根有向树的所有路径诱导类谱半径是积极的加权移位。我们证明了带正权的根有向树上的加权移位允许Wold型分解。我们证明了分解中因子的两两正交性等价于加权移位是平衡的。
英文摘要：
We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the weighted shift. From this fact we deduce reflexivity of those weighted shifts on rooted directed trees whose all path-induced spectral-like radii are positive. We show that weighted shifts with positive weights on rooted directed trees admit a Wold-type decomposition. We prove that the pairwise orthogonality of the factors in the decomposition is equivalent to the weighted shift being balanced.
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