Isometric composition operators on the weighted Hardy spaces
Isometric composition operators on the weighted Hardy spaces
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DOI：
10.1002/mana.200710159
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发表时间：
2010-11
影响因子：
1
通讯作者：
N. Jaoua
中科院分区：
文献类型：
--
作者：
N. Jaoua
研究了加权哈代空间H 2（β）上的复合算子.对于任意有界权序列β，给出了这些算子等距的必要条件.这些条件的充分性在经典空间H2中是众所周知的。在β非减或非增的情况下，它们的充分性仅对极少数加权空间成立。我们找到这样的空间，通过特征的等距单项复合算子，首先对一般的β，然后对任何β如前所述。在不限制β的情况下，我们给出了所有等距复合算子的完整描述.我们还证明了酉单项式的是相同的那些作用在H2。在β有界的情况下，这样的事实延伸到一般符号（© 2010 WILEY-VCH Verlag GmbH & Co. KGaA，魏因海姆）。
We investigate the composition operators on the weighted Hardy spaces H2(β). For any bounded weight sequence β, we give necessary conditions for those operators to be isometric. The sufficiency of those conditions is well‐known for the classical space H2. In the case where β is non‐decreasing or non‐increasing, their sufficiency holds only for very few weighted spaces. We find out such spaces by characterizing the isometric monomial composition operators, first for a general β, then for any β as before. With no restriction on β, we provide a complete description of all isometric composition operators. We also prove that the unitary monomial ones are the same as those acting on H2. Such a fact extends to general symbols in the case where β is bounded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)