Operators on anti-dual pairs: Lebesgue decomposition of positive operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Tarcsay, Zsigmond¹ 

[1] Eotvos Lorand Univ, Dept Appl Anal & Computat Math, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

关键词: Positive operator;    Anti-dual pair;    Lebesgue decomposition;    Absolute continuity;    Singularity;   

DOI  :  10.1016/j.jmaa.2019.123753

来源: Elsevier

【 摘 要 】

In this paper we introduce and study absolute continuity and singularity of positive operators acting on anti-dual pairs. We establish a general theorem that can be considered as a common generalization of various earlier Lebesgue-type decompositions. Different algebraic and topological characterizations of absolute continuity and singularity are supplied and also a complete description of uniqueness of the decomposition is provided. We apply the developed decomposition theory to some concrete objects including operators acting in a rigged Hilbert space, Hermitian forms, representable functionals, and additive set functions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free