Document Zbl 0479.46010

Davis, William J.; Ghoussoub, Nassif; Lindenstrauss, Joram

A lattice renorming theorem and applications to vector-valued processes. (English) Zbl 0479.46010

Trans. Am. Math. Soc. 263, 531-540 (1981).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0479.46010

MSC:

46B42	Banach lattices
46B03	Isomorphic theory (including renorming) of Banach spaces
60G42	Martingales with discrete parameter
46G10	Vector-valued measures and integration

Keywords:

order continuous Banach lattice; renorming; vector-valued processes; martingales; submartingales; ergodic theorem; vector measures; locally uniformly convex norm

Cite Review PDF

Full Text: DOI

References:

[1]	Alexandra Bellow, Les amarts uniformes, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 20, A1295 – A1298 (French, with English summary). · Zbl 0359.60047
[2]	Czesław Bessaga and Aleksander Pełczyński, Selected topics in infinite-dimensional topology, PWN — Polish Scientific Publishers, Warsaw, 1975. Monografie Matematyczne, Tom 58. [Mathematical Monographs, Vol. 58]. · Zbl 0304.57001
[3]	S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach spaces., Math. Scand. 22 (1968), 21 – 41. · Zbl 0175.14503 · doi:10.7146/math.scand.a-10868
[4]	Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. · Zbl 0268.46013
[5]	Joseph Diestel, Geometry of Banach spaces — selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. · Zbl 0307.46009
[6]	J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. · Zbl 0369.46039
[7]	N. Ghoussoub and J. Michael Steele, Vector-valued subadditive processes and applications in probability, Ann. Probab. 8 (1980), no. 1, 83 – 95. · Zbl 0426.60032
[8]	Henri Heinich, Convergence des sous-martingales positives dans un Banach réticulé, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 5, A279 – A280 (French, with English summary). · Zbl 0383.60046
[9]	W. B. Johnson and L. Tzafriri, On the local structure of subspaces of Banach lattices, Israel J. Math. 20 (1975), no. 3-4, 292 – 299. · Zbl 0311.46003 · doi:10.1007/BF02760334
[10]	J. F. C. Kingman, Subadditive processes, École d’Été de Probabilités de Saint-Flour, V – 1975, Springer, Berlin, 1976, pp. 167 – 223. Lecture Notes in Math., Vol. 539.
[11]	Andrzej Korzeniowski, A proof of the ergodic theorem in Banach spaces via asymptotic martingales, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 12, 1041 – 1044 (1979) (Russian). · Zbl 0403.60014
[12]	Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. · Zbl 0403.46022
[13]	Edith Mourier, Eléments aléatoires dans un espace de Banach, Ann. Inst. H. Poincaré 13 (1953), 161 – 244 (French). · Zbl 0053.09503
[14]	Michael Neumann, On the Strassen disintegration theorem, Arch. Math. (Basel) 29 (1977), no. 4, 413 – 420. · Zbl 0368.28013 · doi:10.1007/BF01220429
[15]	J. Neveu, Discrete-parameter martingales, Revised edition, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. Translated from the French by T. P. Speed; North-Holland Mathematical Library, Vol. 10. · Zbl 0345.60026
[16]	Helmut H. Schaefer, Banach lattices and positive operators, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 215. · Zbl 0296.47023

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.