点击次数：

所属单位：理学院

发表刊物：BANACH JOURNAL OF MATHEMATICAL ANALYSIS

关键字：Radon-Nikodym theorem operator-valued measure weak*measure dilation continuous generalized frame

摘要：In this article we determine that an operator-valued measure (OVM) for Banach spaces is actually a weak? measure, and then we show that an OVM can be represented as an operator-valued function if and only if it has sigma-finite variation. By the means of direct integrals of Hilbert spaces, we introduce and investigate continuous generalized frames (continuous operator-valued frames, or simply CG frames) for general Hilbert spaces. It is shown that there exists an intrinsic connection between CG frames and positive OVMs. As a byproduct, we show that a Riesz-type CG frame does not exist unless the associated measure space is purely atomic. Also, a dilation theorem for dual pairs of CG frames is given.

ISSN号：1735-8787

是否译文：否

发表时间：2017-04-01

合写作者：李凤界

通讯作者：李凤界,李鹏同