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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 1, Pages 199–204 (Mi smj1949)  
This article is cited in 6 scientific papers (total in 6 papers)

The Kreps–Yan theorem for Banach ideal spaces

D. B. Rokhlin

Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences
Full-text PDF (294 kB) Citations (6)
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Abstract: Consider a closed convex cone $C$ in a Banach ideal space $X$ on some measure space with $\sigma$-finite measure. We prove that the fulfilment of the conditions $C\cap X_+=\{0\}$ and $C\supset-X_+$ guarantees the existence of a strictly positive continuous functional on $X$ whose restriction to $C$ is nonpositive.
Keywords: Kreps–Yan theorem, Banach ideal space, $\sigma$-finite measure, cone, separation.
Received: 11.10.2007
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 1, Pages 162–166
DOI: https://doi.org/10.1007/s11202-009-0018-3
Bibliographic databases:
UDC: 517.982.22
Language: Russian
Citation: D. B. Rokhlin, “The Kreps–Yan theorem for Banach ideal spaces”, Sibirsk. Mat. Zh., 50:1 (2009), 199–204; Siberian Math. J., 50:1 (2009), 162–166
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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