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Schwartz, Laurent

The three operators theorem. (Le théorème des trois opérateurs.) (French) Zbl 0909.60036

Ann. Math. Blaise Pascal 3, No. 1, 143-164 (1996).
The author proves the following main results: Let \(E,F,G,H\) be Banach spaces, \(F\) is reflexive and separable, \(G\) is reflexive; \(u:E\to F\), and \(v:F\to G\) are linear continuous functions “0-radonifiante”, \(w:G\to H\) is 1-summable. If \(L\) is a cylindrical semi-martingale with values in \(E\), \(L\in {\mathcal L} (E';{\mathcal S} {\mathcal M})\) is a local semi-martingale with values in \(H\). If \(L\) is a semi-martingale with values in \(H\) and satisfies the Radon-Nikodym properties (in particular is reflexive), then \(wvu(L) \in{\mathcal S} {\mathcal M} (H)\).
Reviewer: S.Wedrychowicz (Rzeszów)

Cited in 1 Review
Cited in 2 Documents

MSC:

60G44 Martingales with continuous parameter
60B05 Probability measures on topological spaces
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\textit{L. Schwartz}, Ann. Math. Blaise Pascal 3, No. 1, 143--164 (1996; Zbl 0909.60036)
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References:

[1] Grothendieck, Alexandre,[1] “Produits Tensoriels Topologiques et Espaces Nucléaires”, Memoirs of the American Mathematical Society, 1955. · Zbl 0123.30301
[2] Maurey, Bernard, [1], “Théorèmes de factorisation pour les applications linéaires à valeurs dans les espaces Lp”, chapitre V, Astérisque n° 11. · Zbl 0278.46028
[3] Schwartz, Laurent [1]: “Applications radonifiantes”, séminaire Schwartz, Ecole Polytechnique, Centre de Mathématiques, 1969-1970. · Zbl 0195.13003
[4] Schwartz, Laurent [2]: “Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures”, Tata Institute of Fundamental Research, Oxford University Press, 1973. · Zbl 0298.28001
[5] Schwartz, Laurent [3]: “Théorie des Distributions à Valeurs Vectorielles”, Annales de l’Institut Fourier, chapitre I, tome VII, 1957, et chapitre II, tome VIII, 1958. · Zbl 0089.09801
[6] Schwartz, Laurent, [4], “Les semi-martingales formelles”, Séminaire de Probabilités XV, 1979-80, , 850, pages 413-489. · Zbl 0464.60058
[7] Schwartz, Laurent,[5], “Semi-martingales à Valeurs dans des Espaces d”Applications C∞ entre Espaces Vectoriels (I), Comptes Rendus de l’Académie des Sciences de Paris, tome 305, Série I, pages 49-53, 1987; et Le Théorème Φ-1, et les Semi- Martingales à Valeurs dans des Espaces d’Applications C∞ entre Variétés(II), C. R. Acad. Sc. Paris, tome 305, Série I, p. 49-53, 1987. · Zbl 0617.60051
[8] Ustunel, Ali Süleyman[1], “A characterization of semi-martingales on nuclear spaces”, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete”, 60, pages 21-39,1982. · Zbl 0466.60006
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