Geodesic
Hölder equality for conditional expectations with application to linear monotone operators
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 194-198 Cet article a éte moissonné depuis la source Math-Net.Ru

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In a standard space $L_p=L_p(\Omega,\mathfrak{A},P)$, $1\le p<\infty$, for a given factor $f$ and a $\sigma$-algebra $\mathfrak{B}\subseteq\mathfrak{A} $, a certain criterion is derived for a conditional expectation $x(X)=E(Xf\,|\,\mathfrak{B})$ to represent a continuous linear operator over $X\in L_p$. As an application, the above representation (with the corresponding factor $f\ge 0$) is considered for a general linear monotone operator $x(X)$, $X\in K$, given on an arbitrary subcone $K\subseteq L_p^+ $ in $L_p^+ =\{X\in L_p:X\ge 0\}$.
Keywords: conditional expectations, linear monotone operators, linear monotone extensions.
Mots-clés : Hölder inequality 
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G. Di Nunno. Hölder equality for conditional expectations with application to linear monotone operators. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 194-198. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a13/

[1] Albeverio S., Rozanov Yu. A., “On multi-period market extension with the uniformly equivalent martingale measure”, Acta. Appl. Math., 67:3 (2001), 253–275 | DOI | MR | Zbl

[2] Dinculeanu N., Vector Measures, Pergamon Press, Oxford, 1967, 432 pp. | MR

[3] Di Nunno G., Rozanov Yu. A., On monotone versions of Hahn–Banach extension theorem, IAMI 99.11, CNR, Milano, 1999

[4] Fuchssteiner B., Lusky W., Convex Cones, North-Holland, Amsterdam, 1981, 429 pp. | MR | Zbl

[5] Kreps D. M., “Arbitrage and equilibrium in economics with infinitely many commodities”, J. Math. Econom., 8:1 (1981), 15–35 | DOI | MR | Zbl

[6] Schaefer H. H., Banach Lattices and Positive Operators, Springer-Verlag, New York, 1974, 376 pp. | MR | Zbl

[7] Yosida K., Functional Analysis, Springer-Verlag, Berlin, Heidelberg, 1980, 501 pp. | MR | Zbl