Measurable linear functionals and operators on Fréchet spaces
HTML articles powered by AMS MathViewer
- by Andrzej Wiśniewski PDF
- Proc. Amer. Math. Soc. 114 (1992), 1079-1085 Request permission
Abstract:
The structure of measurable linear functionals and operators on Fréchet spaces with so-called stochastic bases is described.References
- R. H. Cameron and Ross E. Graves, Additive functionals on a space of continuous functions. I, Trans. Amer. Math. Soc. 70 (1951), 160–176. MR 40590, DOI 10.1090/S0002-9947-1951-0040590-8
- Đặng Hùng Thắng and Nguyen Zui Tien, On symmetric stable measures with discrete spectral measure on Banach spaces, Probability theory on vector spaces, II (Proc. Second Internat. Conf., Błażejewko, 1979) Lecture Notes in Math., vol. 828, Springer, Berlin, 1980, pp. 286–301. MR 611731
- Wojciech Herer, Stochastic bases in Fréchet spaces, Demonstratio Math. 14 (1981), no. 3, 719–724 (1982). MR 663121
- J. Hoffmann-Jørgensen, Integrability of seminorms, the $0-1$ law and the affine kernel for product measures, Studia Math. 61 (1977), no. 2, 137–159. MR 464382, DOI 10.4064/sm-61-2-137-159
- Kiyosi Itô and Makiko Nisio, On the convergence of sums of independent Banach space valued random variables, Osaka Math. J. 5 (1968), 35–48. MR 235593
- Marek Kanter, Random linear functionals and why we study them, Vector space measures and applications (Proc. Conf., Univ. Dublin, Dublin, 1977) Lecture Notes in Math., vol. 645, Springer, Berlin-New York, 1978, pp. 114–123. MR 502433
- Michel Loève, Probability theory, 3rd ed., D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. MR 0203748 Nguen Zui Tien, The structure of measurable linear functionals for Gaussian measures on Banach spaces, Teor. Veroyatnost. i Primenen. 23 (1978), 165-168. (Russian)
- Yoshiaki Okazaki, Stochastic basis in Fréchet space, Math. Ann. 274 (1986), no. 3, 379–383. MR 842619, DOI 10.1007/BF01457222
- A. V. Skorohod, Integration in Hilbert space, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 79, Springer-Verlag, New York-Heidelberg, 1974. Translated from the Russian by Kenneth Wickwire. MR 0466482, DOI 10.1007/978-3-642-65632-3
- Kazimierz Urbanik, Random linear functionals and random integrals, Colloq. Math. 33 (1975), no. 2, 255–263, 304. MR 400324, DOI 10.4064/cm-33-2-255-263
- Andrzej Wiśniewski, Measurable linear operators on Banach spaces, Colloq. Math. 54 (1987), no. 2, 261–265. MR 948518, DOI 10.4064/cm-54-2-261-265 —, Measurable linear functionals and operators on Fréchet spaces, Fifth Internat. Vilnius Conf. on Probab. Theory Math. Stat., Abstracts of Comm., T.II, Vilnius, 1989, pp. 227-228.
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 1079-1085
- MSC: Primary 60B11; Secondary 46G12, 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1992-1100667-4
- MathSciNet review: 1100667