Complex Symmetric Operators and Applications II
Complex Symmetric Operators and Applications II
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DOI：
10.1090/s0002-9947-05-03742-6
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发表时间：
2005-05
影响因子：
1.3
通讯作者：
S. Garcia;M. Putinar
中科院分区：
文献类型：
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作者：
S. Garcia;M. Putinar
复希尔伯特空间H上的有界线性算子T称为复对称的，如果T = CT*C，其中C是共轭（H的等距反线性对合）。我们证明了T = CJ\T|，其中J是辅助共轭，与|不|= 10T *T。我们考虑了许多例子，包括庞加莱-诺依曼奇异积分（有界）算子和约旦模型算子（压缩移位）。分解T = CJ\T|也扩展到类的无界C-自伴算子，最初介绍了Glazman。在这方面，它提供了一种方法，估计某些无界算子的预解式的范数。
A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT*C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ\T|, where J is an auxiliary conjugation commuting with |T| = √T*T. We consider numerous examples, including the Poincare-Neumann singular integral (bounded) operator and the Jordan model operator (compressed shift). The decomposition T = CJ\T| also extends to the class of unbounded C-selfadjoint operators, originally introduced by Glazman. In this context, it provides a method for estimating the norms of the resolvents of certain unbounded operators.