Affiliation of Author(s):理学院
Journal:BANACH JOURNAL OF MATHEMATICAL ANALYSIS
Key Words:Radon-Nikodym theorem operator-valued measure weak*measure dilation continuous generalized frame
Abstract: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 No.:1735-8787
Translation or Not:no
Date of Publication:2017-04-01
Co-author:李凤界
Correspondence Author:李凤界,lpt
Date of Publication:2017-04-01