Generalized Riesz Systems and Quasi Bases in Hilbert Space
Generalized Riesz Systems and Quasi Bases in Hilbert Space
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希尔伯特空间中的广义Riesz系统和准基
DOI：
10.1007/s00009-019-1456-1
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发表时间：
2019
影响因子：
1.1
通讯作者：
C. Trapani
中科院分区：
文献类型：
--
作者：
F. Bagarello;H. Inoue;C. Trapani
本文的目的是双重的。首先，对Hilbert空间的稠密子空间对引入-拟基的概念。它由两个双正交序列和组成，使得对所有和。其次，证明了如果双正交序列和构成a-拟基，则它们是广义Riesz系统。后者在非自伴哈密顿算子和其他物理相关算子的构造中起着有趣的作用。
The purpose of this article is twofold. First of all, the notion of-quasi basis is introduced for a pairof dense subspaces of Hilbert spaces. This consists of two biorthogonal sequencesand, such thatfor alland. Second, it is shown that if biorthogonal sequencesandform a-quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators.