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arXiv · 2409.14068

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

Ábel Göde·Zsigmond Tarcsay
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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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Ábel Göde, Zsigmond Tarcsay. 2024-09-21. Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration. https://arxiv.org/abs/2409.14068

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