A Hahn-Jordan decomposition and Riesz-Frechet representation theorem in Riesz spaces
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Publication:6132181
DOI10.2989/16073606.2023.2287843arXiv2209.00715OpenAlexW4392594697MaRDI QIDQ6132181
Author name not available (Why is that?)
Publication date: 18 April 2024
Published in: (Search for Journal in Brave)
Abstract: We give a Hahn-Jordan decomposition in Riesz spaces which generalizes that of [{{sc B. A. Watson}, {An And^o-Douglas type theorem in Riesz spaces with a conditional expectation,} {em Positivity,} {�f 13} (2009), 543 - 558}] and a Riesz-Frechet representation theorem for the -strong dual, where is a Riesz space conditional expectation operator. The result of Watson was formulated specifically to assist in the proof of the existence of Riesz space conditional expectation operators with given range space, i.e., a result of And^{o}-Douglas type. This was needed in the study of Markov processes and martingale theory in Riesz spaces. In the current work, our interest is a Riesz-Frechet representation theorem, for which another variant of the Hahn-Jordan decomposition is required.
Full work available at URL: https://arxiv.org/abs/2209.00715
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