单元算子的共轭，I

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2024-05-16 DOI:10.1007/s13324-024-00924-z

Javad Mashreghi, Marek Ptak, William T. Ross

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引用次数: 0

摘要

如果 U 是可分离复希尔伯特空间上的一个单元算子，那么应用谱定理就可以知道在 \(\mathcal {H}\) 上存在一个共轭 C（\(\mathcal {H}/\)上的一个反线性、非卷积、等势），对于这个共轭 C，\( C U C = U^{*}.\在本文中，我们将固定一个单元算子 U，并描述所有满足这一性质的共轭 C。我们的结果表明，当且仅当一个子空间对于任意共轭 C 都是不变的（\(CUC = U^{*}\)），那么这个子空间对于 U 就是超不变的。

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Conjugations of unitary operators, I

If U is a unitary operator on a separable complex Hilbert space \(\mathcal {H}\), an application of the spectral theorem says there is a conjugation C on \(\mathcal {H}\) (an antilinear, involutive, isometry on \(\mathcal {H}\)) for which \( C U C = U^{*}.\) In this paper, we fix a unitary operator U and describe all of the conjugations C which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for U if and only if it is invariant for any conjugation C for which \(CUC = U^{*}\).

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.