Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration

2024/09/21 by Ábel Göde, Göde, Ábel, Zsigmond Tarcsay +1
Computer Science · Mathematics · #47A07 #47B65 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2409.14068

openalex publication_date 2024/09/21 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass several special cases, including positive operators on Hilbert spaces, non-negative forms on vector spaces, and representable functionals over *-algebras.

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